Chapter 14 Review Questions

14. What is an Arrhenius plot? Explain the significance of the slope and intercept of an Arrhenius plot.

An Arrhenius plot is a plot of the natural log of the rate constant (lnk) versus the inverse of the temperature in kelvin (1/T). It yields a straight line with a slope of -Ea/R and a y-intercept of lnA.

23. What are enzymes? What is the active site of an enzyme? What is a substrate?

Enzymes are biological catalysts that increase the rates of biochemical reactions. Enzymes are large protein molecules with complex three-dimensional structures. Within that structure is a specific area called the active site. The properties and shape of the active site are just right to bind the reactant molecule, usually called the substrate. The substrate fits into the active site in a manner that is analogous to a key fitting into a lock.

20. What is a catalyst? How does a catalyst increase the rate of a chemical reaction?

A catalyst is a substance that increases the rate of a chemical reaction but is not consumed by the reaction. A catalyst works by providing an alternative mechanism for the reaction—one in which the rate-determining step has a lower activation energy.

17. In a reaction mechanism, what is an elementary step? Write down the three most common elementary steps and the corresponding rate law for each one.

An elementary step is a single step in the reaction mechanism; cannot be broken down into simpler steps; they occur as they are written; they're characterized by their molecularity, the number of reactant particles involved in the step. The molecularity of the three most common types of elementary steps are as followed: unimolecular A→products and Rate= k[A]; bimolecular A+A→products and Rate = k[A]² and bimolecular A+B→products and Rate = k[A][B]. Elementary steps in which three reactant particles collide, called termolecular steps are very rare because the probability of three particles simultaneously colliding is small.

18. What are the two requirements for a proposed mechanism to be valid for a given reaction?

For a proposed reaction mechanism to be valid: (1) the elementary steps in the mechanism must sum to the overall reaction, and (2) the rate law predicted by the mechanism must be consistent with the experimentally observed rate law.

6. Consider a simple reaction in which reactant A forms products: A -> products What is the rate law if the reaction is zero order with respect to A? First order? Second order? For each case, explain how a doubling of the concentration of A would affect the rate of reaction.

For a zero-order reaction, Rate = k [A]⁰ = k; so doubling the concentration of A does nothing to the reaction rate. For a first-order reaction, Rate = k[A]¹ = k[A]; so doubling the concentration of A doubles the reaction rate. For a second-order reaction, Rate = k[A]²; so doubling the concentration of A quadruples the reaction rate.

22. What are the four basic steps involved in heterogeneous catalysis?

Heterogeneous catalysis (involving solid catalysts) occurs by the following four-step process: (1) adsorption—the reactants are adsorbed onto the solid surface, (2) diffusion—the reactants diffuse on the surface until they approach each other, (3) reaction—the reactants react to form the products, and (4) desorption—the products desorb from the surface into the gas phase.

21. Explain the difference between homogeneous catalysis and heterogeneous catalysis.

In homogeneous catalysis, the catalyst exists in the same phase as the reactants. In heterogeneous catalysis, the catalyst exists in a phase different from that of the reactants. The most common type of heterogeneous catalyst is a solid catalyst.

15. Explain how a chemical reaction occurs according to the collision model. Explain the meaning of the orientation factor in this model.

In the collision model, a chemical reaction occurs after a sufficiently energetic collision between the two reactant molecules. In collision theory, therefore, each approach to the activation barrier is a collision between the reactant molecules. The value of the frequency factor should simply be the number of collisions that occur per second. In the collision model, k = p z e^-Ea/RT, where the frequency factor (A) has been separated into two separate parts—p is called the orientation factor, and z is the collision frequency. The collision frequency is simply the number of collisions that occur per unit time. The orientation factor says that if two molecules are to react with each other, they must collide in such a way that allows the necessary bonds to break and form. The small orientation factor indicates that the orientational requirements for this reaction are fairly stringent—the molecules must be aligned in a very specific way for the reaction to occur. When two molecules with sufficient energy and the correct orientation collide, something unique happens: The electrons on one of the atoms or molecules are attracted to the nuclei of the other; some bonds begin to weaken, and other bonds begin to form. If all goes well, the reactants go through the transition state and are transformed into the products and a chemical reaction occurs.

4. Why is the reaction rate for reactants defined as the negative of the change in reactant concentration with respect to time, whereas for products it is defined as the change in reactant concentration with respect to time (with a positive sign)?

Reactant concentrations decrease as a reaction proceeds; therefore, the change in the concentration of a reactant is negative. Thus, the negative sign in the definition makes the overall rate positive. The negative sign is the result of the convention that reaction rates are usually reported as positive quantities. Because the product concentrations are increasing, the concentration of a product divided by the change in time is positive.

19. What is an intermediate within a reaction mechanism?

Reaction intermediates are species that are formed in one step of a mechanism and consumed in another step. They're not found in the balanced equation for the overall reaction, but play a key role in the mechanism.

7. How is the order of a reaction generally determined?

The reaction order cannot be determined by the stoichiometry of the reaction. It can only be determined by running controlled experiments where the concentrations of the reactants are varied and the reaction rates are measured and analyzed.

5. Explain the difference between the average rate of reaction and the instantaneous rate of reaction.

The average rate of the reaction can be calculated for any time interval as Rate = -1/a x ([A]t2-[A]t1/ t2 -t1) for the chemical reaction aA + bB -> cC + dD. The instantaneous rate of the reaction is the rate at any one point in time, represented by the instantaneous slope of the plot of concentration versus time at that point. We can obtain the instantaneous rate from the slope of the tangent to this curve at the point of interest.

24. What is the general two-step mechanism by which most enzymes work?

The general mechanism by which an enzyme (E) binds a substrate (S) and then reacts to form the products (P) is as follows: (1) E + S <=> ES (fast) and (2) ES -> E + P (slow, rate-limiting).

13. Explain the meaning of each term within the Arrhenius equation: activation energy, frequency factor, and exponential factor. Use these terms and the Arrhenius equation to explain why small changes in temperature can result in large changes in reaction rates.

The modern form of the Arrhenius equation, which relates the rate constant (k) and the temperature in kelvin (T), is as follows: k = A e^-Ea/RT, where R is the gas constant (8.314 J/mol x K), A is a constant called the frequency factor (or the pre-exponential factor), and Ea is called the activation energy (or activation barrier). The frequency factor is the number of times the reactants approach the activation barrier per unit time. The exponential factor (-Ea/RT) is the fraction of approaches that are successful in surmounting the activation barrier and forming products. The exponential factor increases with increasing temperature, but decreases with an increasing value for the activation energy. As the temperature increases, the number of collisions increases and the number of molecules having enough thermal energy to surmount the activation barrier increases. Under common circumstances, only a small fraction of the molecules have enough energy to make it over the activation barrier. Because of the shape of the energy distribution curve, however, a small change in temperature results in a large difference in the number of molecules having enough energy to surmount the activation barrier.

16. Explain the difference between a normal chemical equation for a chemical reaction and the mechanism of that reaction.

The overall equation shows the substances present at the beginning of the reaction and the substances formed by the reaction—it does not show the intermediate steps that may be involved. A reaction mechanism is a series of individual chemical steps by which an overall chemical reaction occurs.

9. Explain the difference between the rate law for a reaction and the integrated rate law for a reaction. What relationship does each kind of rate law express?

The rate law shows the relationship between the rate of a reaction and the concentrations of the reactants. The integrated rate law for a chemical reaction is a relationship between the concentration of a reactant and time.

3. What units are typically used to express the rate of a reaction?

The rate of a chemical reaction is measured as a change in the amounts of reactants or products (usually in terms of concentration) divided by the change in time. Typical units are molarity per second (M/s), molarity per minute (M/min), and molarity per year (M/yr), depending on how fast the reaction proceeds.

12. How do reaction rates typically depend on temperature? What part of the rate law is temperature dependent?

The rates of chemical reactions are, in general, highly sensitive to temperature. Reaction rates increase as the temperature increases. The temperature dependence of the reaction rate is contained in the rate constant (k), which is actually a constant only when the temperature remains constant.

2. Why are reaction rates important (both practically and theoretically)?

The rates of chemical reactions, and especially the ability to control those rates, are important phenomena in our everyday lives. For example, the human body's ability to switch a specific reaction on or off at a specific time is achieved largely by controlling the rate of that reaction through the use of enzymes. Chemical kinetics is an important subject to chemists and engineers. The launching of a rocket depends on controlling the rate at which fuel burns—too quickly and the rocket can explode, too slowly and it will not leave the ground. The rate of nuclear decay in a nuclear power plant must be carefully controlled to provide electricity safely and efficiently. Chemists must consider reaction rates when synthesizing compounds. No matter how stable a compound might be, its synthesis is impossible if the rate at which it forms is too slow. As we have seen with reptiles, reaction rates are important to life.

1. Explain why lizards become sluggish in cold weather. How is this phenomenon related to chemistry?

Unlike mammals, which actively regulate their body temperature through metabolic activity, lizards are ectotherms—their body temperature depends on their surroundings. When splashed with cold water, a lizard's body gets colder. The drop in body temperature immobilizes the lizard because its movement depends on chemical reactions that occur within its muscles, and the rates of those reactions—how fast they occur—are highly sensitive to temperature. In other words, when the temperature drops, the reactions that produce movement occur more slowly; therefore, the movement itself slows down.