Table of Contents

How to Use this Book

Introduction to the MCAT

PART I: Review

Chapter 1: Atomic Structure

Practice Questions

Chapter 2: The Periodic Table

Practice Questions

Chapter 3: Bonding and Chemical Interactions

Practice Questions

Chapter 4: Compounds and Stoichiometry

Practice Questions

Chapter 5: Chemical Kinetics and Equilibrium

Practice Questions

Chapter 6: Thermochemistry

Practice Questions

Chapter 7: The Gas Phase

Practice Questions

Chapter 8: Phases and Phase Changes

Practice Questions

Chapter 9: Solutions

Practice Questions

Chapter 10: Acids and Bases

Practice Questions

Chapter 11: Redox Reactions and Electrochemistry

Practice Questions

Chapter 12: High-Yield Problem Solving Guide for General Chemistry

Kaplan has been preparing premeds for the MCAT for more than 40 years. In the past 15 years alone, we’ve helped more than 400,000 students prepare for this important exam and improve their chances for medical school admission.

Kaplan MCAT General Chemistry, along with the other four books in our MCAT Subject series, brings the Kaplan classroom experience to you—right in your home, at your convenience. This book offers the same Kaplan content review, strategies, and practice that make Kaplan the #1 choice for MCAT prep. All that’s missing is the teacher.

The Medical College Admission Test (MCAT) is different from any other test you’ve encountered in your academic career. It’s not like the knowledge-based exams from high school and college, where emphasis was on memorizing and regurgitating information. Medical schools can assess your academic prowess by looking at your transcript. The MCAT isn’t even like other standardized tests you may have taken, where the focus was on proving your general skills.

Well, here’s the little secret no one seems to want you to know: The MCAT is not just a science test; it’s also a thinking test. This means that the test is designed to let you demonstrate your thought process, not only your thought content.

Review

Protons are found, along with neutrons, in the nucleus of an atom. Each proton has an amount of charge equal to the fundamental unit of charge (1.6 × 10^-19 C), and we denote this fundamental unit of charge as “+1” for the proton. Protons have a mass of approximately one atomic mass unit, or amu. The atomic number (Z) of an element is equal to the number of protons found in an atom of that element. The atomic number is like your Social Security number; it acts as a unique identifier for each element because no two elements have the same one. All atoms of a given element have the same atomic number, although, as we will see, they do not necessarily have the same atomic mass.

Neutrons are the Switzerland of an atom; they are neutral, which means that they have no charge. A neutron’s mass is only slightly larger than that of the proton, and together, the protons and the neutrons of the nucleus make up almost the total mass of an atom. Every atom has a characteristic mass number, which is the sum of the protons and neutrons in the atom’s nucleus. The number of neutrons in the nuclei of atoms of a given element may vary; thus, atoms of the same element will always have the same atomic number but will not necessarily have the same mass number. Atoms that share an atomic number but have different mass numbers are known as isotopes of the element. The convention is used to show both the atomic number (Z) and the mass number (A) of atom X.

If you think of the nucleus as a game of checkers, the electrons would be children who express varying degrees of interest in playing or watching the game. Electrons move around in pathways in the space surrounding the nucleus and are associated with varying levels of energy. Each electron has a charge equal to that of a proton but with the opposite (negative) charge, denoted by “-1.” The mass of an electron is approximately that of a proton. Because subatomic particle masses are so small, the electrostatic force of attraction between the unlike charges of the proton and electron is far greater than the gravitational force of attraction based on their respective masses.

Bridge

The valence, or outer, electrons will be very important to us in both General and Organic Chemistry. Knowing how tightly held those electrons are will allow us to understand many of an atom’s properties and how it interacts with other atoms.

Going back to our checkers analogy, consider how children form rough circles surrounding a game of checkers; the children sitting closer to the game are more interested in it than the children who are sitting on the periphery. Similarly, electrons are placed in pathways of movement that are progressively farther and farther from the nucleus. The electrons closer to the nucleus are at lower (electric potential) energy levels, while those that are in the outer regions (or shells) have higher energy. Furthermore, if you’ve ever seen children sitting around a game, you know that the “troublemakers” are more likely to sit on the periphery, which allows them to take advantage of an opportunity for mischief when it arises—and so it is also for electrons. Those in the outermost energy level, or shell, called the valence electrons, experience the least electrostatic draw to their nucleus and so are much more likely to become involved in bonds with other atoms (filling empty spaces in other atoms’ valence shells). Generally speaking, the valence electrons determine the reactivity of an atom. In the neutral state, there are an equal number of protons and electrons; a gain of electron(s) results in the atom gaining a negative charge, while a loss of electron(s) results in the atom gaining a positive charge. A positively charged atom is a cation, and a negatively charged atom is an anion.

As we’ve seen, the mass of one proton is defined as approximately one amu. The size of the atomic mass unit is defined as exactly the mass of the carbon-12 atom, approximately 1.66 × 10^-24 grams (g). Because the carbon-12 nucleus has six protons and six neutrons, an amu is really the average of the mass of a proton and a neutron. Because the difference in mass between the proton and the neutron is so small, the mass of the proton and the neutron are each about equal to 1 amu. Thus, the atomic mass of any atom is simply equal to the mass number (sum of protons and neutrons) of the atom. A more common convention used to define the mass of an atom is the atomic weight. The atomic weight is the mass in grams of one mole of atoms of a given element and is expressed as a ratio of grams per mole (g/mol). A mole is the number of “things” equal to Avogadro’s number: 6.022 × 10²³. For example, the atomic weight of carbon is 12 g/mol, which means that 6.022 × 10²³ carbon atoms (1 mole of carbon atoms) have a combined mass of 12 grams (see Chapter 4, Compounds and Stoichiometry). One gram is then equal to one mole of amu.

Mnemonic

Mole Day is celebrated at 6:02 on October 23 (6:02 on 10/23) because of Avogadro’s number (6.02 × 10²³). We will revisit this number in Chapter 4 when we discuss moles in more detail.

The term isotope comes from the Greek, meaning “the same place.” Isotopes are atoms of the same element (hence, occupying the same place on the periodic table of the elements) that have different numbers of neutrons (which means that these atoms of the same element have different mass numbers). Isotopes are referred to by the name of the element followed by the mass number (e.g., carbon-12 has six neutrons, carbon-13 has seven neutrons, etc.). Only the three isotopes of hydrogen are given unique names: protium (Greek protos; first) has one proton and an atomic mass of 1 amu; deuterium (Greek deuteros; second) has one proton and one neutron and an atomic mass of 2 amu; tritium (Greek tritos; third) has one proton and two neutrons and an atomic mass of 3 amu. Because isotopes have the same number of protons and electrons, they generally exhibit the same chemical properties.

Danish physicist Niels Bohr, in 1913, used the work of Rutherford and Planck to develop his model of the electronic structure of the hydrogen atom. Starting from Rutherford’s findings, Bohr assumed that the hydrogen atom consisted of a central proton around which an electron traveled in a circular orbit and that the centripetal force acting on the electron as it revolved around the nucleus was the electrical force between the positively charged proton and the negatively charged electron.

MCAT Expertise

When we see a formula in our review or on Test Day, we need to focus on ratios and relationships rather than the equation as a whole. This simplifies our “calculations” to a conceptual understanding, which is usually enough to lead us to the right answer.

Bohr used Planck’s quantum theory to correct certain assumptions that classical physics made about the pathways of electrons. Classical mechanics postulates that an object revolving in a circle, such as an electron, may assume an infinite number of values for its radius and velocity. The angular momentum (L = mvr) and kinetic energy (KE = ½mv²) of the object, therefore, can take on any value. However, by incorporating Planck’s quantum theory into his model, Bohr placed restrictions on the value of the angular momentum of the electron revolving around the hydrogen nucleus. Analogous to quantized energy, the angular momentum of an electron, Bohr predicted, is quantized according to the following equation:

The Bohr model of the hydrogen atom (and other one-electron systems, such as He⁺ and Li²⁺) is useful for explaining the atomic emission spectrum and atomic absorption spectrum of hydrogen, and it is helpful in the interpretation of the spectra of other atoms.

Modern atomic theory postulates that any electron in an atom can be completely described by four quantum numbers: n, l, m_l, m_s. Furthermore, according to the Pauli exclusion principle, no two electrons in a given atom can possess the same set of four quantum numbers. The position and energy of an electron described by its quantum numbers is known as its energy state. The value of n limits the value of l, which in turn limits the values of m_l. Think of this like a country: A country has a defined number of states, and each state has a defined number of cities or towns. The values of the quantum numbers qualitatively give information about the orientation of the orbital. As we examine the four quantum numbers more closely, pay attention especially to l and m_l, as these two tend to give students the greatest difficulty.

Principal Quantum Number

The first quantum number is commonly known as the principal quantum number and is denoted by the letter n. This is the quantum number used in Bohr’s model that can theoretically take on any positive integer value. The larger the integer value of n, the higher the energy level and radius of the electron’s orbit(al). Within each shell of some n value, there is a capacity to hold a certain number of electrons equal to 2n², and the capacity to hold electrons increases as the n value increases. The difference in energy between two shells decreases as the distance from the nucleus increases because the energy difference is a function of [1/n_i² - 1/n_f²]. For example, the energy difference between the n = 3 and the n = 4 shells is less than the energy difference between the n = 1 and the n = 2 shells. The term shell brings to mind the notion of eggshells, and you’ve probably heard the analogy between n values and eggshells of increasing size. This is fine as long as you don’t extend the analogy to the point that you are thinking about electron pathways as precisely defined orbits. Nevertheless, if thinking about eggshells helps you to remember that the principal quantum number says something about the overall energy of the electron orbitals as a function of distance from the nucleus, then go with it.

For a given atom or ion, the pattern by which subshells are filled and the number of electrons within each principal energy level and subshell are designated by its electron configuration. In this notation, the first number denotes the principal energy level, the letter designates the subshell, and the superscript gives the number of electrons in that subshell. For example, 2p⁴ indicates that there are four electrons in the second ( p) subshell of the second principal energy level. By definition, this also implies that the energy levels below 2p (that is, 1s and 2s) have already been filled (see Figure 1.3).

MCAT Expertise

Remember that the shorthand used to describe the electron configuration is derived directly from the quantum numbers.

To write out an atom’s electron configuration, you need to know the order in which subshells are filled. They are filled from lower to higher energy, and each subshell will fill completely before electrons begin to enter the next one. You don’t really need to memorize this ordering because there are two very helpful ways of recalling this. The (n + l ) rule can be used to rank subshells by increasing energy. This rule states that the lower the sum of the values of the first and second quantum numbers (n + l ), the lower the energy of the subshell. This is a very helpful rule to remember for Test Day. If two subshells possess the same (n + l ) value, the subshell with the lower n value has a lower energy and will fill with electrons first. The other helpful way to recall this ordering is the flow diagram in Figure 1.3, which also gives the order in which electrons will fill the shells and subshells. We recommend that you quickly write out this flow diagram on the scratch material provided at the testing center at the start of your Physical Science section for quick and easy reference throughout the section.

MCAT Expertise

Remember this chart for Test Day—being able to re-create it quickly on your scratch paper may save you some time and get you that higher score!

The valence electrons of an atom are those electrons that are in its outermost energy shell, most easily removed, and available for bonding. As with the unruly children sitting farthest from the checkers game who are most likely to get themselves into trouble, the valence electrons are the “active” electrons of an atom and to a large extent dominate the chemical behavior of the atom. For elements in Groups IA and IIA (Groups 1 and 2), only the outermost s subshell electrons are valence electrons. For elements in Groups IIIA through VIIIA (Groups 13 through 18), the outermost s and p subshell electrons in the highest principal energy level are valence electrons. For transition elements, the valence electrons are those in the outermost s subshell and in the d subshell of the next-to-outermost energy shell. For the inner transition elements (that is, those in the lanthanide and actinide series), the valence electrons include those in the s subshell of the outermost energy level, the d subshell of the next-to-outermost energy shell, and the f subshell of the energy shell two levels below the outermost shell. All elements in period 3 and below may accept electrons into their d subshell, which allows them to hold more than eight electrons in their valence shell, in apparent “violation” of the octet rule (see Chapters 2 and 3). We’ll learn that this is perfectly acceptable for these elements, however, and is occasionally preferred.

Mnemonic

Remember that paramagnetic means that a magnetic field will cause parallel spins in unpaired electrons and therefore cause an attraction.

Congratulations! You’ve made it through the first chapter, and as far as we can tell, you’re still alive and there seems to have been minimal shedding of tears and blood. Good! Now that we have covered topics related to the most fundamental unit of matter, the atom, you’re set to advance your understanding of the physical world in more complex ways. This chapter described the characteristics and behavior of the three subatomic particles—the proton, the neutron, and the electron. In addition, it compared and contrasted the two most recent models of the atom. The Bohr model is adequate for describing the structure of one-electron systems, such as the hydrogen atom or the helium ion, but fails to describe adequately the structure of more complex atoms. The quantum mechanical model theorizes that electrons are found, not in discrete-pathway orbits, but in “clouds of probability,” or orbitals, by which we can predict the likelihood of finding electrons within given regions of space surrounding the nucleus. Both theories tell us that the energy levels available to electrons are not infinite but discrete and that the energy between levels is a precise amount called a quantum. The four quantum numbers completely describe the position and energy of any electron within a given atom. Finally, we learned two simple recall methods for the order in which electrons fill the shells and subshells of an atom and that the valence electrons are the troublemakers in an atom—and the ones we need to keep our eyes on.

CONCEPTS TO REMEMBER

1. Which orbital fills first: 4s or 3d ? Which is first to give up electrons?

2. Why do atoms have neutrons? What purpose do they serve?

Explanations to Practice Questions

If we imagine one atom of any element to essentially be a little cloud of electrons with a dense core of protons and neutrons, then the atomic radius of an element is equal to one-half the distance between the centers of two atoms of that element that are just touching each other. (We can’t measure atomic radius by examining a single atom because the electrons are constantly moving around and it becomes impossible to mark the outer boundary of the electron cloud.) As we move across a period from left to right, protons and electrons are added one at a time to the atoms. Because the electrons are being added only to the outermost shell and the number of inner-shell electrons (which act as insulation between the nucleus and the valence electrons) remains constant, the increasing positive charge of the nucleus holds the outer electrons more closely and more tightly. The Z_eff increases left to right across a period, and as a result, atomic radius decreases from left to right across a period.

MCAT Expertise

As an electron and a proton get farther away from one another, it becomes easier to pull them apart. This will help us understand all the trends with respect to the radius.

As we move down a group, the increasing principal quantum number implies that the valence electrons will be found farther away from the nucleus because the number of inner shells is increasing, separating the valence shell from the nucleus. Although the Z_eff remains essentially constant, atomic radius increases in a group from top to bottom. In summary, within each group, the largest atom will be at the bottom, and within each period, the largest atom will be within Group IA (Group 1).

Ionization energy (IE), also known as ionization potential, is the energy required to remove an electron completely from a gaseous atom or ion. Removing an electron from an atom always requires an input of energy (it’s always endothermic; Chapter 6). Anybody who has ever volunteered to make fundraising calls for a nonprofit organization knows that considerable energy must be invested in convincing a person to give a charitable donation, no matter how charitable the potential donor may be. Some are easier to convince than others are, but in the end, every donation is secured by a lot of hard work, effective communication, and skillful playing of the guilt and pity cards. The higher the atom’s Z_eff or the closer the valence electrons are to the nucleus, the more tightly they are bound to the atom. This makes it more difficult to remove one or more electrons, so the ionization energy increases. Thus, ionization energy increases from left to right across a period and decreases in a group from top to bottom. Furthermore, the subsequent removal of a second or third electron requires increasing amounts of energy, because the removal of more than one electron necessarily means that the electrons are being removed from an increasingly cationic species. The energy necessary to remove the first electron is called the first ionization energy; the energy necessary to remove the second electron from the univalent cation to form the divalent cation is called the second ionization energy, and so on. For example:

Mg(g) Mg⁺(g) + e^- First Ionization Energy = 7.646 eV

Mg⁺(g) Mg²⁺(g) + e^- Second Ionization Energy = 15.035 eV

Elements in Groups I and II (Groups 1 and 2) have such relatively low ionization energies that they are called the active metals. The active metals never exist naturally in their neutral elemental (native) forms; they are always found in ionic compounds, minerals, or ores. The loss of one electron (from the alkali metals) or the loss of two electrons (from the alkaline earth metals) results in the formation of a stable, filled valence shell. As you might imagine from the trend, the Group VIIA (Group 17) elements, the halogens, are a miserly group of penny pinchers and aren’t willing to give up their electrons to anybody. In fact, in their monatomic ion form, they are found only as anions, having greedily taken one electron from another atom to complete their octets. As you might guess, the halogens have very large ionization energies and the smaller the halogen atom, the higher the ionization energy.

The greedy halogens are among the worst of the bunch of elements that tend to hoard their electrons toward themselves. These elements also tend to be very anxious to gain the number of electrons necessary to complete their octets. Like nervous little squirrels frantically running around in search of nuts to pack into their accommodating cheek pouches, these elements go in search of other atoms that are willing to give up their electrons. When a gaseous atom of a particular elemental identity gains one or more electrons to complete its octet, it relaxes and breathes a sigh of relief. This “sigh of relief ” is a release of a quantity of energy called the electron affinity. Because energy is released when an atom gains an electron, we can describe this process as exothermic. By convention, the electron affinity is reported as a positive energy value, even though by the conventions of thermodynamics, exothermic processes have negative energy changes. Regardless of the sign, just remember that electron affinity is released energy. The stronger the electrostatic pull (that is, the Z_eff) between the nucleus and the valence shell electrons, the greater the energy release will be when the atom gains the electron. Thus, electron affinity increases across a period from left to right. Because the valence shell is farther away from the nucleus as the principal quantum number increases, electron affinity decreases in a period from top to bottom. Groups IA and IIA (Group 1 and 2) have very low electron affinities, preferring rather to give up one or two electrons, respectively, to achieve the octet configuration of the prior noble gas. Group VIIA (Group 17) elements have very high electron affinities because they need to gain only one electron to achieve the octet configuration of the immediately following noble gases in Group VIIIA (Group 18). Although the noble gases are the group of elements farthest to the right and would be predicted to have the highest electron affinities according to the trend, they actually have electron affinities on the order of zero, since they already possess a stable octet and cannot readily accept an electron. Elements of other groups generally have low electron affinity values.

Mnemonic

To recall the various trends, remember this: Cesium, Cs, is the largest, most metallic, and least electronegative of all naturally occurring elements. It also has the smallest ionization energy and the least exothermic electron affinity.

No, we are not referring to pessimistic electrons. Electronegativity is a measure of the attractive force that an atom will exert on an electron in a chemical bond. The greater the electronegativity of an atom, the greater is its attraction for bonding electrons. Electronegativity values are related to ionization energies: The lower the ionization energy, the lower the electronegativity; the higher the ionization energy, the higher the electronegativity. The electronegativity value for any element is not measured directly and there are different scales used to express it. The most common scale is the Pauling electronegativity scale, which ranges from 0.7 for cesium, the least electronegative (most electropositive) element, to 4 for fluorine, the most electronegative element. Electronegativity increases across a period from left to right and decreases in a period from top to bottom. Figure 2.1 Summarizes the behavior of atoms in terms of the periodic table.

MCAT Expertise

Electronegativity might better be called “nuclear positivity.” it is a result of the nucleus’ attraction for electrons; that is, the Z_eff perceived by the electrons in a bond.

Metals, found both on the left side and in the middle of the periodic table, include the active metals, the transition metals, and the lanthanide and actinide series of elements. Metals are shiny solids, except for mercury, which is a liquid under standard state conditions. They generally have high melting points and densities, but there are exceptions, such as lithium, which has a density that is about half that of water. Metals have the ability to be deformed without breaking; the ability of metal to be hammered into shapes is called malleability, and its ability to be drawn into wires is called ductility. At the atomic level, low Z_eff, low electronegativity (high electropositivity), large atomic radius, and low ionization energy define metals. These characteristics make it fairly easy for metals to give up one or more electrons. Many of the transition metals, for example, are known to have two oxidation states, and some have more than that. Because the valence electrons of all metals are only loosely held to their atoms, they are essentially free to move, which makes metals generally good conductors of heat and electricity (some are better than others). The valence electrons of the active metals are found in the s subshell, those of the transition metals are found in the d subshell, and those of the lanthanide and actinide series elements are found in the f subshell. Some transition metals—such as copper, nickel, silver, gold, palladium, and platinum—are relatively nonreactive, a property that makes them ideal substances for the production of coins and jewelry.

MCAT Expertise

The effective nuclear charge, Z_eff, can explain all periodic trends as well as chemical properties.

Nonmetals are found on the upper right side of the periodic table. The metals claim that the nonmetals are jealous of them for their shiny hair and sparkly personalities. The nonmetals scoff back, yet quietly steal electrons from them. Nonmetals are generally brittle in the solid state and show little or no metallic luster. They have high ionization energies, electron affinities, and electronegativities; have small atomic radii; and are usually poor conductors of heat and electricity. Nonmetals are less unified in their chemical and physical properties than are the metals. They are separated from the metals by a diagonal band of elements called the metalloids.

The metalloids are also called the semimetals because they possess characteristics that are between those of metals and nonmetals. The electronegativities and ionization energies of the metalloids lie between those of metals and nonmetals. Their physical properties, such as densities, melting points, and boiling points, vary widely and can be combinations of metallic and nonmetallic characteristics. For example, silicon has a metallic luster but is brittle and a poor conductor. The particular reactivity of the metalloids is dependent upon the elements with which they are reacting. Boron (B), for example, behaves as a nonmetal when reacting with sodium (Na) and as a metal when reacting with fluorine (F). The elements classified as metalloids form a “staircase” on the periodic table and include boron, silicon, germanium, arsenic, antimony, tellurium, and polonium.

Real World

Metalloids share some properties with metals, and others with nonmetals. For instance, metalloids make good semiconductors due to their electrical conductivity.

The alkali metals, Group IA (Group 1), possess most of the classic physical properties of metals, except that their densities are lower than those of other metals (as is true of lithium). The alkali metals have only one loosely bound electron in their outermost shells, and their Z_eff values are very low, giving them the largest atomic radii of all the elements in their respective periods. The very low Z_eff values also result in low ionization energies, low electron affinities, and low electronegativities, and these atoms easily lose one electron to form univalent cations. They react very readily with nonmetals, especially halogens.

Key Concept

Alkali and alkaline earth metals are both metallic in nature because they both lose electrons easily from the s-orbital of their valence shells.

The alkaline earth metals, Group IIA (Group 2), also possess many properties characteristic of metals. They share most of the characteristics of the alkali metals, except that they have slightly higher effective nuclear charges and so have slightly smaller atomic radii. They have two electrons in their valence shell, both of which are easily removed to form divalent cations. Together, the alkali and alkaline earth metals are called the active metals because they are so reactive that they are not naturally found in their elemental (neutral) state.

The halogens, Group VIIA (Group 17), are highly reactive nonmetals with seven valence electrons. They are rather “desperate” to complete their octets by each gaining an additional electron. The halogens are highly variable in their physical properties. For instance, the halogens range from gaseous (F₂ and Cl₂) to liquid (Br₂) to solid (I₂) at room temperature. Their chemical reactivity is more uniform, and due to their very high electronegativities and electron affinities, they are especially reactive toward the alkali and alkaline earth metals. Fluorine has the highest electronegativity of all the elements. The halogens are so reactive that they are not naturally found in their elemental state but rather as ions (called halides).

MCAT Expertise

Halogens are seen often on the MCAT. Remember that they only need one more electron to become “noble” (have that full valence shell).

The noble gases, Group VIIIA (Group 18), are also known as the inert gases because they have very low chemical reactivities as a result of their filled valence shells. They have high ionization energies, little or no tendency to gain or lose electrons, and no real electronegativities. They are essentially snobby elements, as they refuse to mingle with the hoi polloi. After all, they already have everything they need. The noble gases have low boiling points, and all exist as gases at room temperature.

The transition elements, Groups IB to VIIIB (Groups 3 to 12), are all considered metals and as such have low electron affinities, low ionization energies, and low electronegativities. These metals are very hard and have high melting and boiling points. They tend to be quite malleable and are good conductors due to the loosely held electrons that are progressively filling the d subshell orbitals in the valence shell. One of the unique properties of the transition metals is that many of them can have different possible charged forms, or oxidation states, because they are capable of losing various numbers of electrons from the s- and d-orbitals of the valence shell. For instance, copper (Cu), in Group 1B (Group 11), can exist in either the +1 or the +2 oxidation state, and manganese (Mn), in Group VIIB (Group 7), can have the +2, +3, +4, +6, or +7 oxidation state. Because of this ability to attain different positive oxidation states, transition metals form many different ionic and partially ionic compounds. The dissolved ions can form complex ions either with molecules of water (hydration complexes) or with nonmetals, forming highly colored solutions and compounds (e.g., CuSO₄·5H₂O), and this complexation may enhance the relatively low solubility of certain compounds. For example, AgCl is insoluble in water but quite soluble in aqueous ammonia due to the formation of the complex ion [Ag(NH₃)₂]⁺. The formation of complexes causes the d-orbitals to split into two energy sublevels. This enables many of the complexes to absorb certain frequencies of light—those containing the precise amount of energy required to raise electrons from the lower to the higher d sublevel. The frequencies not absorbed (known as the subtraction frequencies) give the complexes their characteristic colors.

MCAT Expertise

Transition metals are present in biological systems and are therefore often seen on the MCAT (think iron in hemoglobin). You don’t need to memorize them, but be able to use your knowledge from these first two chapters to understand how the transition metals ionize and act.

Now that we have completed our review of the periodic table of the elements, commit to understanding (not just to memorizing) the trends of physical and chemical properties that will allow you to answer quickly the questions on the MCAT. You will find, as you progress through the chapters of this book, that your foundational understanding of the elements will help you develop a richer, more nuanced understanding of their general and particular behaviors. Topics in general chemistry that may have given you trouble in the past will be understandable from the perspective of the behaviors and characteristics that you have reviewed here.

CONCEPTS TO REMEMBER

1. Mercury (Hg) exists as a liquid at room temperature. Why, then, is it classified as a metal? What metallic properties might it possess?

2. The transition metals in group VIIIB could theoretically have eight different oxidation states. In reality, that does not hold true. Why not?

Explanations to Practice Questions

The formation of one covalent bond may not be sufficient to fill the valence shell for a given atom. Thus, many atoms can form bonds with more than one other atom, and each atom can form multiple bonds between itself and another atom, with few exceptions. Two atoms sharing one, two, or three pairs of electrons are said to be joined by a single, double, or triple covalent bond, respectively. The number of shared electron pairs between two atoms is called the bond order; hence, a single bond has a bond order of one, a double bond has a bond order of two, and a triple bond has a bond order of three. Three features characterize a covalent bond: bond length, bond energy, and polarity.

Bond Length

If the arrangement of atoms in covalent bonds can be likened to two wooden spools connected by a dowel in a very sophisticated children’s construction set, then the length of the dowel is analogous to the length of the bond between the atoms sharing the electron pair(s). Bond length is the average distance between the two nuclei of the atoms involved in the bond. As the number of shared electron pairs increases, the two atoms are pulled closer together, leading to a decrease in bond lengths. Thus, for a given pair of atoms, a triple bond is shorter than a double bond, which is shorter than a single bond.

Bridge

We will see a great example of covalent bonds in organic chemistry, and we can see here the inverse proportionality between bond length and strength.

In a coordinate covalent bond, the shared electron pair comes from the lone pair of one of the atoms in the molecule, while the other atom involved in the bond contributes nothing to the relationship. (This works great for atoms but might not be the best way to form a lasting marriage!) Once such a bond forms, however, it is indistinguishable from any other covalent bond. The distinction is only helpful for keeping track of the valence electrons and formal charges (see Figure 3.2). Coordinate covalent bonds are typically found in Lewis acid-base compounds (see Chapter 10, Acids and Bases). A Lewis acid is any compound that will accept a lone pair of electrons, while a Lewis base is any compound that will donate a pair of electrons to form a covalent bond; for example, as in the reaction between borontrifluoride (BF₃) and ammonia (NH₃) shown in Figure 3.2.

The electrons that are involved in a covalent bond are in the valence shell and are called bonding electrons, while those electrons in the valence shell that are not involved in the covalent bond are called nonbonding electrons. The unshared electron pairs can also be called lone electron pairs, because they are associated only with one atomic nucleus. Because atoms can bond with other atoms in many different possible combinations, the Lewis structure system of notation has been developed to keep track of the bonded and nonbonded electron pairs. You may think of Lewis structures as a kind of bookkeeping. The number of valence electrons attributed to a particular atom in the Lewis structure of a molecule is not necessarily the same as the number of valence electrons the atom would have as an isolated atom, and the difference accounts for what is referred to as the formal charge of that atom in a particular Lewis structure. Often, more than one Lewis structure can be drawn for a molecule. If the possible Lewis structures differ in the way the atoms are connected (that is to say, they differ in their bond connectivity or arrangement), then the Lewis structures represent different possible compounds. If the Lewis structures show the same bond connectivity and differ only in the arrangement of the electron pairs, then these structures represent different resonance forms for a single compound. Lewis structures do not represent the actual or even theoretical geometry of a real compound. Their usefulness lies in showing you the different possible ways in which atoms may be combined to form different compounds or resonances of a single compound. When more than one arrangement can be made, you can assess the likelihood of each arrangement by checking the formal charges on the atoms in each arrangement. The arrangement that minimizes the number of formal charges, or minimizes the value of formal charges, is the arrangement that most likely represents the actual compound.

Key Concept

When dealing with Lewis dot structures, we only deal with the eight valence electrons (s- and p-orbitals of the outer shell) on each atom. Remember that some atoms can expand their octets by utilizing the d-orbitals in this outer shell, but this will only take place with atoms in period 3 or greater.

Lewis Structures

A Lewis structure, or Lewis dot symbol, is the chemical symbol of an element surrounded by dots, each representing one of the s and/or p valence electrons of the atom. The Lewis symbols of the elements in the second period of the periodic table are shown in Table 3.1.

Table 3.1

Because Lewis structures do not in any way suggest or reflect the actual geometric arrangement of atoms in a compound, we need another system that provides that information. One such system is known as valence shell electron pair repulsion theory (VSEPR theory). This theory is actually dependent upon Lewis structure, so they go hand in hand.

To finish our discussion of covalent bonds, we need to address the issue of atomic and molecular orbitals. If you remember back to the first chapter, we described the modern understanding of the atom as a dense, positively charged nucleus surrounded by clouds of electrons organized into orbitals (regions in space surrounding the nucleus within which there are certain probabilities of finding an electron). The four quantum numbers completely describe the energy and position of any electron of an atom. While the principal quantum number indicates the average energy level of the orbitals, the azimuthal quantum number, l, describes the subshells within each principal energy level, n. When l = 0, this indicates the s-subshell, which has one orbital that is spherical in shape. The 1s-orbital (n = 1, l = 0) is plotted in Figure 3.8.

Bridge

Quantum Numbers (Chapter 1) revisited:

• For any value of n, there are n values of l(0n- 1).

•

l= 0s

The bonding electrons in nonpolar covalent bonds may appear, on paper, to be shared equally between two atoms, but at any point in time, they will be located randomly throughout the orbital. For these instantaneous moments, then, the electron density may be unequally distributed between the two atoms. This results in rapid polarization and counterpolarization of the electron cloud and the formation of short-lived dipole moments. These dipoles interact with the electron clouds of neighboring compounds, inducing the formation of more dipoles. The momentarily negative end of one molecule will cause the closest region in any neighboring molecule to become temporarily positive itself, thus causing the other end of this neighboring molecule to become temporarily negative, which in turn induces other molecules to become temporarily polarized, and the entire process begins all over again. The attractive interactions of these short-lived and rapidly shifting dipoles are called dispersion forces or London forces.

Real World

While London forces (a type of van der Waals force) are the weakest of the intermolecular attractions, when there are millions of these interactions, as there are on the bottom of a gecko’s foot, there is an amazing power of adhesion, which is demonstrated by the animal’s ability to climb smooth vertical, even inverted, surfaces.

Dispersion forces are the weakest of all the intermolecular interactions because they are the result of induced dipoles that change and shift moment by moment. They do not extend over long distances and are, therefore, significant only when molecules are close together. The strength of the London force also depends on the degree to which and the ease by which the molecules can be polarized (that is to say, how easily the electrons can be shifted around). Large molecules in which the electrons are far from the nucleus are relatively easy to polarize and, thus, possess greater dispersion forces. Think about two plates—a big dinner plate and a small teacup saucer—with nearly equal numbers of marbles on each. The marbles will roll around more, and may be distributed more unequally, on the bigger plate than on the smaller saucer. Nevertheless, don’t underestimate the importance of the dispersion forces. If it weren’t for them, the noble gases would not liquefy at any temperature because no other intermolecular forces exist between the noble gas atoms. The low temperatures at which the noble gases liquefy is to some extent indicative of the magnitude of the dispersion forces between the atoms.

Polar molecules tend to orient themselves in such a way that the opposite ends of the respective molecular dipoles are closest to each other: The positive region of one molecule is close to the negative region of another molecule. This arrangement is energetically favorable because an attractive electrostatic force is formed between the two molecules.

Hydrogen bonds are a favorite of the MCAT! So understand them well, and you will be able to answer every question pertaining to their nature, behavior, and effects. A hydrogen bond is actually only a specific, unusually strong form of dipole–dipole interaction, which may be intra- or intermolecular. Please understand that hydrogen bonds are not actually bonds—there is no sharing or transfer of electrons between two atoms. When hydrogen is bound to a highly electronegative atom, such as fluorine, oxygen, or nitrogen, the hydrogen atom carries little of the electron density of the covalent bond. The hydrogen atom acts essentially as a naked proton (it is a little scandalous!). The positively charged hydrogen atom interacts with the partial negative charge of oxygen, nitrogen, or fluorine on nearby molecules. Substances that display hydrogen bonding tend to have unusually high boiling points compared with compounds of similar molecular formula that do not hydrogen bond. The difference derives from the energy required to break the hydrogen bonds. A very good example of this difference, which you absolutely need to understand for the MCAT, is the difference between a carboxylic acid, which can form hydrogen bonds between molecules of itself, and the acyl halide, a derivative of the carboxylic acid, which has substituted a halogen for the hydroxyl group and which cannot form hydrogen bonds with molecules of itself. The boiling point of propanoic acid (MW = 74 g/mol) is 141°C, but the boiling point of propanoyl chloride (MW = 92.5 g/mol) is 80°C. Hydrogen bonding is particularly important in the behavior of water, alcohols, amines, and carboxylic acids. It is no overstatement to say that if it weren’t for water’s ability to form hydrogen bonds and exist in the liquid state at room temperature, we would not exist (at least not in the form we recognize as “human”).

This chapter built upon our knowledge of the atom and the trends demonstrated by the elements in the periodic table to understand the different ways by which atoms partner together to form compounds, either (a) exchanging electrons to form ions, which are then held together by the electrostatic force of attraction that exists between opposite charges, or (b) sharing electrons to form covalent bonds. We discussed the nature and characteristics of covalent bonds, noting their relative lengths and energies as well as polarities. The review of Lewis structures and VSEPR theory will prepare you for predicting likely bond arrangements, resonance structures, and molecular geometry. Finally, we compared the relative strengths of the most important intermolecular electrostatic interactions, noting that even the strongest of these, the hydrogen bond, is still much weaker than an actual covalent bond. The next time you’re searing meat in a skillet or browning toast in a toaster, take a moment to consider what’s actually going on at the atomic and molecular level. It’s not just cooking; it’s science!

CONCEPTS TO REMEMBER

1. Why does bond length decrease with increasing bond strength?

2. Predict two elements whose hydrides (H^-) would contain incomplete octets.

Explanations to Practice Questions

We’ve mentioned already that the term atomic weight is a misnomer, because it is a measurement of mass, not weight (another distinction not worth any sacrifice of sleep), and the same applies here to our discussion of molecular weight: It’s really a measurement of mass. Molecular weight, then, is simply the sum of the atomic weights of all the atoms in a molecule, and its units are atomic mass units (amu). Similarly, the formula weight of an ionic compound is found by adding up the atomic weights of the constituent ions according to its empirical formula (see the following example), and its units are grams.

Example: What is the molecular weight of SOCl₂?

Solution: To find the molecular weight of SOCl₂, add together the atomic weights of each of the atoms.

We defined the term mole in Chapter 1, Atomic Structure, but let’s briefly review it. A mole is a quantity of any thing (molecules, atoms, dollar bills, chairs, etc.) equal to the number of particles that are found in 12 grams of carbon-12. That seems like an awfully strange point of comparison, so all you really need to remember is that “mole” is a quick way of indicating that we have an amount of particles equal to Avogadro’s number, 6.022 × 10²³. One mole of a compound has a mass in grams equal to the molecular weight of the compound expressed in amu and contains 6.022 × 10²³ molecules of that compound. For example, 62 grams of H₂CO₃ (carbonic acid) represents one mole of the acid compound and contains 6.022 × 10²³ molecules of H₂CO₃. The mass of one mole of a compound, called its molar weight or molar mass, is usually expressed as g/mol. Therefore, the molar mass of H₂CO₃ is 62 g/mol. You may be accustomed to using the term molecular weight to imply molar mass. Technically this is not correct, but nobody is going to rap your knuckles with a ruler for this minor infraction.

Equivalent weight and the related concept of equivalents are a source of confusion for many students. Part of the problem may be the context in which equivalents and equivalent weights are discussed: acid-base reactions, redox reactions, and precipitation reactions, all three of which themselves can be sources of much student confusion and anxiety. So let’s start with some very basic discussion, and then, in later chapters, we will see how these concepts and calculations apply to these three types of reactions.

Bridge

The idea of equivalents is similar to the concept of normality, which we will see when we study Acids and Bases in Chapter 10.

Generally, some compounds or elements have different capacities to act in certain ways, not in terms of their characteristics or behaviors, like electronegativity or ionization energy, but rather the ability of certain elements or compounds to act more potently than others in performing certain reactions. For example, one mole of HCl has the ability to donate one mole of hydrogen ions (H⁺) in solution, but one mole of H₂SO₄ has the ability to donate two moles of hydrogen ions, and one mole of H₃PO₄ has the ability to donate three moles of hydrogen ions. Another example to consider is the difference between Na and Mg: One mole of sodium has the ability to donate one mole of electrons, while one mole of magnesium has the ability to donate two moles of electrons. To find one mole of hydrogen ions for a particular acid-base reaction, we could “source” those protons from one mole of HCl, or we could instead use a half-mole of H₂SO₄. If we’re using H₃PO₄, we’d only need one-third of a mole. This is what we mean by “different capacities to act in certain ways.” If we need only one mole of hydrogen ions, it would be a waste to use an entire mole of H₃PO₄, which could donate three times what we need. We are defining the concept of equivalents: How many moles of the “thing we are interested in” (i.e., protons, hydroxide ions, electrons, or ions) will the number of moles of the compound present produce? One mole of hydrogen ions (one equivalent) will be donated by one mole of HCl, but two moles of hydrogen ions (two equivalents) will be donated by one mole of H₂SO₄, and three moles of hydrogen ions (three equivalents) will be donated by one mole of H₃PO₄. Simply put, an equivalent is a mole of charge.

The law of constant composition states that any pure sample of a given compound will contain the same elements in the identical mass ratio. For example, every sample of H₂O will contain two hydrogen atoms for every one oxygen atom, or in terms of mass, for every one gram of hydrogen, there will be eight grams of oxygen. We’re sorry to say that it doesn’t matter whether the water you drink is sourced from deep springs in the Fiji Islands or flows out of a tap connected to a shallow well. The law of constant composition says that water is water.

There are two ways to express a formula—the elemental composition—for a compound. The empirical formula gives the simplest whole number ratio of the elements in the compound. The molecular formula gives the exact number of atoms of each element in the compound and is usually a multiple of the empirical formula. For example, the empirical formula for benzene is CH, while the molecular formula is C₆H₆. For some compounds, the empirical and molecular formulas are the same, as in the case of H₂O. For the reasons previously discussed, ionic compounds, such as NaCl or CaCO₃, will only have empirical formulas.

The percent composition by mass of an element is the weight percent of a given element in a specific compound. To determine the percent composition of an element X in a compound, the following formula is used:

% Composition = (Mass of X in formula/Formula weight of compound) × 100%

You can calculate the percent composition of an element by using either the empirical or the molecular formula; just be sure to use to the appropriate mass measurement:

MCAT Expertise

Percent composition is a common way for stoichiometry to be tested on the MCAT. Practice these problems to build up speed and efficiency for Test Day.

formula weight for empirical formula or molar mass for molecular formula. Formula weight is simply the mass of the atoms in the empirical formula of a compound.

A combination reaction has two or more reactants forming one product. The formation of sulfur dioxide by burning sulfur in air is an example of a combination reaction.

S (s) + O₂ (g) SO₂ (g)

A decomposition reaction is the opposite of a combination reaction: A single compound reactant breaks down into two or more products, usually as a result of heating or electrolysis. An example of decomposition is the breakdown of mercury (II) oxide. (The [delta] sign over a reaction arrow represents the addition of heat.)

Sometimes one atom in a molecule gets tired of the other (“I love you, but I’m not in love with you…”), and divorce becomes inevitable when something better comes along. This is a single-displacement reaction: an atom (or ion) of one compound is replaced by an atom of another element. For example, zinc metal will displace copper ions in a copper sulfate solution to form zinc sulfate.

Zn (s) + CuSO₄ (aq) Cu (s) + ZnSO₄

Single-displacement reactions are often further classified as redox reactions, which will be discussed in great detail in Chapter 11, Redox Reactions and Electrochemistry. Not to carry the analogy to the point of ridiculousness, but just to make the point: Cu in CuSO₄ has an oxidation state of +2, but when it leaves the compound, it gains two electrons (the Cu⁺² is reduced to Cu)—you may think of this as Cu⁺² getting an alimony settlement or gaining back its dignity for leaving that no-good cheater, SO₄^2-. On the other side, Zn loses its dignity (in the form of two electrons) when it desperately throws itself into the arms of SO₄^2-.

Well, if you think atoms are acting scandalously in single-displacement reactions, just wait until you get a load of the atomic depravity in double-displacement reactions. In double-displacement reactions, also called metathesis, elements from two different compounds swap places with each other (hence, the name double-displacement) to form two new compounds. This type of reaction occurs when one of the products is removed from the solution as a precipitate or gas or when two of the original species combine to form a weak electrolyte that remains undissociated in solution. For example, when solutions of calcium chloride and silver nitrate are combined, insoluble silver chloride forms in a solution of calcium nitrate.

CaCl₂ (aq) + 2AgNO₃ (aq) Ca(NO₃)₂ (aq) + 2AgCl (s)

Neutralization reactions are a specific type of double displacement in which an acid reacts with a base to produce a salt. For example, hydrochloric acid and sodium, hydroxide will react to form sodium chloride and water.

HCl (aq) + NaOH NaCl (aq) + H₂O

We began our consideration of compounds with a particularly odoriferous one: benzaldehyde. As a compound, it is made from constituent atoms of different elements in a set ratio defined by its empirical or molecular formula. Each molecule of a compound has a defined mass that is measured as its molecular weight. The mass of one mole of any compound is determined from its molar mass in the units of grams/mole. We reviewed the basic classifications of reactions commonly tested on the MCAT: combination, decomposition, single-displacement, and double-displacement reactions. Furthermore, we are now confident in our understanding of the steps necessary to balance any chemical reaction; we are ready to tackle more stoichiometric problems in preparation for Test Day.

1. Can the Law of Constant Composition be applied to solutions?

2. What is the purpose of calculating a reactant’s gram equivalent weight?

Explanations to Practice Questions

Very rarely is the balanced reaction equation, with which we work to calculate limiting reactants and yields, an accurate representation of the actual steps involved in the chemical process from reactants to products. Many reactions proceed by more than one step, the series of which is known as the mechanism of a reaction and the sum of which gives the overall reaction (the one that you, typically, are asked to balance). When you know the accepted mechanism of a reaction, this helps you explain the reaction’s rate, position of equilibrium, and thermodynamic characteristics (see Chapter 6). Consider this generic reaction:

Overall reaction: A₂ + 2B 2AB

If we consider a generic reaction, 2A + B C, in which one mole of C is produced from every two moles of A and one mole of B, we can describe the rate of this reaction in terms of either the disappearance of reactants over time or the appearance of products over time. Because the reactants, by definition, are being consumed in the process of formation of the products, we place a minus sign in front of the rate expression in terms of reactants. For the previous reaction, the rate of the reaction with respect to A is -[A]/t, with respect to B is -[B]/t, and with respect to C is [C]/t. You’ll notice that the stoichiometric coefficients for the reaction are not equal, and this tells you that the rates of change of concentrations are not equal. Because two moles of A are consumed for every mole of B consumed, rate _-[A] = 2 rate_-[B]. Furthermore, for every two moles of A consumed, only one mole of C is produced; thus, we can say that the rate_-[A] = 2 rate_[C]. Based on the stoichoimetry, you can see that the rate of consumption of B is equal to the rate of production of C. To show a standard rate of reaction in which the rates with respect to all reaction species are equal, the rate of concentration change of each species should be divided by the species’ stoichiometric coefficient:

Here’s something you can take to the bank (that is, to the MCAT testing center): In the Physical Sciences section of the MCAT, it is extremely unlikely that the test maker will give you a reaction equation that you can merely look at and write the correct rate law. Therefore, on the MCAT, whenever you are asked to determine the rate law for a reaction in which you are given the net equation, the first thing you will do is look for experimental data.

MCAT Expertise

Remember that the stoichiometric coefficients for the overall reaction will most likely be different from those for the rate-determining step and will, therefore, not be the same as the order of the reaction.

However, we’re getting ahead of ourselves, so let’s start with the basics. For nearly all forward, irreversible reactions, the rate is proportional to the product of the concentrations of the reactants, each raised to some power. For the general reaction

aA + bB cC + dD

the rate is proportional to [A]^x[B]^y. By including a proportionality constant, k, we can say that rate is determined according to the following equation:

rate = k[A]^x[B]^y

This expression is called the rate law for the general reaction shown here, where k is the reaction rate coefficient or rate constant. Rate is always measured in units of concentration over time; that is, molarity/second. The exponents x and y (or x, y, and z, if there are three reactants, etc.) are called the orders of the reaction: x is the order with respect to reactant A, and y is order with respect to reactant B. The overall order of the reaction is the sum of x + y (+ z...). These exponents may be integers, fractions, or zero and must be determined experimentally. The MCAT will focus almost entirely on zero-, first-, second-, and third-order reactions only. Furthermore, in most cases, the exponents will be integers.

We classify chemical reactions on the basis of kinetics into classes of reactions called zero-order, first-order, second-order, mixed-order, or higher-order reactions. We will continue to consider the generic reaction aA + bB cC + dD for this discussion.

Zero-Order Reactions

A zero-order reaction is one whose rate of formation of product C is independent of changes in concentrations of any of the reactants, A and B. These reactions have a constant reaction rate equal to the rate coefficient (rate constant) k. The rate law for a zero-order reaction is

rate = k[A]⁰[B]⁰ = k

where k has units of M·s^-1. (Remember that any number raised to the zero power equals 1.) We will remind you that the rate constant itself is dependent upon temperature; thus, it is possible to change the rate for a zero-order reaction by changing the temperature. The only other way to change the rate of a zero-order reaction is by the addition of a catalyst, which lowers the energy of activation, thereby increasing the value of k.

MCAT Expertise

Temperature is the only factor that can change the rate of a zero-order reaction.

First-Order Reactions

A first-order reaction (order = 1) has a rate that is directly proportional to only one reactant, such that doubling the concentration of, say, reactant A results in a doubling of the rate of formation of product C. The rate law for a first-order reaction is

rate = k[A]¹ or rate = k[B]¹

where k has units of s^-1. A classic example of a first-order reaction is the process of radioactive decay. From the rate law, in which the rate of decrease of the amount of a radioactive isotope A is proportional to the amount of A,

It’s one thing to say “A₂ reacts with B₂ to form 2AB”; it’s quite another to be able to describe, as precisely as possible, the actual interactions that occur between A₂ and B₂ to produce AB at some rate. Various theories have been proposed to explain the events that are taking place at the atomic level through the process of a reaction.

Collision Theory of Chemical Kinetics

For a reaction to occur, molecules must collide with each other in much the same way that for children to enjoy themselves, there usually must be some rough physical contact involved; that is, of course, until someone’s eye gets poked out. The collision theory of chemical kinetics states that the rate of a reaction is proportional to the number of collisions per second between the reacting molecules.

If you imagine a group of children playing together in a rough-and-tumble game of tag, we can identify certain conditions that would result in a more vigorous, more fun, more effective game. We can use this analogy to remember the factors that can affect chemical reaction rates.

Reactant Concentrations

A group of children playing tag will probably have more fun the greater the number of children playing: The participation of more children equals more opportunities to chase, trip, and tag each other. The greater the concentrations of the reactants, the greater the number of effective collisions per unit time. Therefore, the reaction rate will increase for all but zero-order reactions. For reactions occurring in the gaseous state, the partial pressures of the gas reactants serve as a measure of concentration (see Chapter 7, The Gas Phase).

MCAT Expertise

We saw earlier in this chapter that increasing reactant concentrations might increase the reaction rate, but be aware of each reactant^’s order before making this assumption.

Temperature

You can imagine that children’s enthusiasm for playing tag outside increases as the temperature warms from the bone-chilling snowstorms of winter to the pleasant sun of June. For nearly all reactions, the reaction rate will increase as the temperature increases. Because the temperature of a substance is a measure of the particles’ average kinetic energy, increasing the temperature increases the average kinetic energy of the molecules. Consequently, the proportion of molecules having energies greater than E_a (thus capable of undergoing reaction) increases with higher temperature. You’ll often hear that raising the temperature of a system by 10°C will result in an approximate doubling of the reaction rate. You have to be careful with this approximation, as it is generally true for biological systems but not so for many other systems. (Don’t forget also: If the temperature gets too high, a catalyst may denature—and then the reaction rate plummets!)

For a generic reversible reaction aA + bB cC + dD, the law of mass action states that if the system is at equilibrium at a given temperature, then the following ratio is constant:

The law of mass action defines the position of equilibrium by stating that the ratio of the product of the concentrations of the products, each raised to their respective stoichiometric coefficients, to the product of the concentrations of the reactants, each raised to their respective stoichiometric coefficients, is constant. However, equilibrium is a state that is achieved only through time. Depending on the actual rates of the forward and reverse reactions, equilibrium might be achieved in minutes or years. What can we use as a kind of “timer” that tells us how far along in the process toward equilibrium the reaction has reached? We can take another measurement of concentrations called the reaction quotient, Q_c. At any point in time of a reaction, we can measure the concentrations of all the reactants and products and calculate the reaction quotient according to the following equation:

Remember the following characteristics of the law of mass action and the equilibrium constant expression:

• The concentrations of pure solids and pure liquids (the solvent, really) do not appear in the equilibrium constant expression, because for the purposes of the MCAT, their concentrations do not change in the course of the reaction. (Actually, the concentrations of any pure solids and/or pure liquids are included in the expression, but we assign them a value of 1 and “hide” the actual concentrations by incorporating them into the equilibrium constant.

• K_eq is characteristic of a particular reaction at a given temperature: The equilibrium constant is temperature dependent.

• Generally, the larger the value of K_eq, the farther to the right we’ll find the equilibrium and the more complete the reaction.

• If the equilibrium constant for a reaction written in one direction is K_eq, the equilibrium constant for the reaction written in reverse is 1/K_eq.

When you add or remove reactants or products from a reaction in equilibrium, you are causing the reaction to be no longer at its energy minimum state. Metaphorically, you have pushed the reaction, like a ball, up a little ways along the slope of the energy hills on either side of the energy valley. The actual effect is that with the change in concentration of one or another of the chemical species, you have caused the system to have a ratio of products to reactants that is not equal to the equilibrium ratio. In other words, changing the concentration of either a reactant or a product results in Q_c ≠ K_eq. By adding reactant or removing product, you have created a situation in which Q_c < K_eq, and the reaction will spontaneously move in the forward direction, increasing the value of Q_c until Q_c = K_eq. By removing reactant or adding product, you have created a situation in which Q_c > K_eq, and the reaction will spontaneously react in the reverse direction, thereby decreasing the value of Q_c until once again Q_c = K_eq. A simple way to remember this is: The system will always react in the direction away from the added species or toward the removed species.

Bridge

Remember this equation:

CO₂ + H₂O HCO₃^- + H⁺

In the tissues, there is a lot of CO₂, and the reaction shifts to the right. In the lungs, CO₂ is lost, and the reaction shifts to the left. Note that blowing off CO₂ (hyperventilation) is used as a mechanism of dealing with acidosis (excess H⁺).

We often take advantage of this particular tendency of chemical reactions in order to improve the yield of chemical reactions. For example, where possible in the industrial production of chemicals, products of reversible reactions are removed as they are formed so as to prevent the reactions from ever reaching their equilibrium states. The reaction will continue to go in the forward direction, producing more and more product (assuming continual replenishment of reactants as they are consumed in the reaction). You could also drive a reaction forward by starting with higher concentrations of reactants. This will lead to an increase in the absolute quantities of products formed, but the reaction would still eventually reach its equilibrium state, unless product was removed as it formed.

Because liquids and solids are essentially incompressible, only chemical reactions that involve at least one gas species will be affected by changes to the system’s volume and pressure. When you compress a system, its volume decreases, and the total pressure increases. The increase in the total pressure is associated with an increase in the partial pressures of all the gases in the system, and this results in the system no longer being in the equilibrium state, such that Q_p ≠ K_eq. The system will move either forward or in reverse but always toward whichever side has the lower total number of moles of gas. This result is a consequence of the ideal gas law, which tells us that there is a direct relationship between the number of moles of gas and the pressure of the gas. If you increase the pressure on a system, it will respond by decreasing the pressure by means of decreasing the number of gas moles present. (In this case, the volume of the system was decreased and then held constant while the system returned to its equilibrium state.) When you expand a system, its volume increases, and the total pressure and partial pressures decrease. The system is no longer in its equilibrium state and will react in the direction of the side with the greater number of moles of gas.

Le Châtelier’s principle tells us that changing the temperature of a system will also cause the system to react in a particular way so as to “return” to its equilibrium state, but we have to be careful here, because unlike the effect of changing concentrations or pressures, the result of changing temperature is not simply a change in the reaction quotient, Q_c or Q_p, but a change in K_eq. The change in temperature doesn’t cause the concentrations or partial pressures of the reactants and products to change immediately, so the Q immediately after the temperature change is the same before the temperature change. Before the temperature change, the system was at equilibrium, and Q was equal to K_eq; now after the temperature change, K_eq is a different value (because it depends on temperature), so Q ≠ K_eq. The system has to move in whichever direction allows it to reach its new equilibrium state at the new temperature. That direction is determined by the enthalpy of the reaction (see Chapter 6, Thermochemistry). You can think of heat as a reactant if the reaction is endothermic (+H) and as a product if the reaction is exothermic (-H). Thinking about heat as a reactant or product allows you to apply the principle that we discussed in regards to concentration changes to temperature changes. For example, consider the following exothermic reaction:

A B + heat (-H)

If we placed this system in an ice bath, its temperature would decrease, driving the reaction to the right to replace the heat lost. Conversely, if the system were placed in a boiling water bath, the reaction would shift to the left due to the increased “concentration” of heat. All of this is to say that on Test Day, when you are asked to predict the direction a reaction would go in response to a change in temperature, you must look for the enthalpy change for the reaction, which will be given somewhere in the passage, figure, or question stem.

Key Concept

The reaction

A (aq) + 2 B ( g) C (g) + heat

We’ve discussed some very important concepts and principles in this chapter related to the studies of reaction rates and chemical equilibria. We began with a consideration of chemical reactions and the mechanisms that illustrate the possible individual steps necessary to transform reactants into products. We demonstrated the way to derive a reaction’s rate law through the analysis of experimental data, and we looked at the factors that can affect the rates of chemical reactions. The second part of this chapter focused on the law of mass action and the significance of the equilibrium state of a chemical reaction. With our understanding of the significance of K_eq and Q, we are able to predict the direction that a reaction will go in response to various stresses—concentration, pressure, or temperature changes—that might be applied to a system.

1. Because catalysts affect reaction rate, why don’t we include their concentrations in reaction rate laws?

2. Do zero-order reactions contradict the collision theory of chemical kinetics?

3. How can Le Châtelier’s principle be used to manipulate reactions?

Explanations to Practice Questions

We began our discussion of thermochemistry with a review of different ways in which we characterize systems (isolated, closed, etc.) and processes (adiabatic, isothermal, etc.). We then further classified systems according to their state functions: system properties such as volume, pressure, temperature, enthalpy, entropy, and Gibbs free energy that describe the equilibrium state. We defined enthalpy as the heat content of the system and the change in enthalpy as the change in heat content of the system from one equilibrium state to another. Enthalpy is characterized as the energy found in the intermolecular interactions and in the bonds of the compounds in the system. We explored the various ways Hess’s law can be applied to calculate the total enthalpy change for a series of reactions. Moving on to entropy, we described this property as a measure of the degree to which energy in a system becomes spread out through a process. There is danger in thinking too literally about entropy as “disorder,” as a system’s entropy may be increasing even if there is no observable change in the system’s macroscopic disorder (e.g., ice warming from -10°C to -5°C). Gibbs free energy combines enthalpy and entropy considerations, and the change in Gibbs function determines whether a process will be spontaneous or nonspontaneous. When the change in Gibbs function is negative, the process is spontaneous, but when the change in Gibbs function is positive, the process is nonspontaneous.

1. Why is energy required to break bonds? Why is it released when bonds are formed?

2. Why is H so much easier to determine than instantaneous H (enthalpy)? What standard methods have been developed to help scientists find H through calculations?

3. What is the difference between exergonic and exothermic? What is the difference between endergonic and endothermic?

Explanations to Practice Questions

1. Gases are made up of particles whose volumes are negligible compared to the container volume.

2. Gas atoms or molecules exhibit no intermolecular attractions or repulsions.

3. Gas particles are in continuous, random motion, undergoing collisions with other particles and the container walls.

4. Collisions between any two gas particles are elastic, meaning that there is conservation of both momentum and kinetic energy.

5. The average kinetic energy of gas particles is proportional to the absolute temperature (in Kelvin) of the gas, and it is the same for all gases at a given temperature, irrespective of chemical identity or atomic mass.

It’s fairly straightforward to imagine, based on the assumptions just listed, gas particles as lots of little rubber balls bouncing into and off each other and off the walls of their container. Of course, rubber balls, like real gas particles, have measurable mass and volume, and not even the bounciest rubber balls will collide in a completely elastic manner.

Average Molecular Speeds

According to the kinetic molecular theory of gases, the average kinetic energy of a gas particle is proportional to the absolute temperature of the gas: