Chapter 13

In the substitution reaction of \(\mathrm{Cl}^{-}\) for \(\mathrm{OH}^{-}\) in 2-propanol, explain how \(\mathrm{Zn}^{2+}\) acts as a catalyst to increase the reaction rate.

What is the general name given to biological catalysts?

What is meant by the following terms: (a) Substrate (b) Active site (c) Lock-and-key mechanism

Inhibitors are poisons that permanently stop a catalyst or an enzyme from working. Postulate how they might accomplish this.

In Section \(6.1\), the development of the first antibiotics was described. Was this accomplished by making modified versions of the lock or the key? Explain your answer.

Why are catalysts important to industrial chemical processes? Why are they important to biological chemical processes?

In general, increasing the concentration of a reactant will usually increase the rate of a reaction. Why is this true?

Why would decreasing the volume of a container in which a gas-phase reaction is taking place speed up the reaction?

Does the rate constant \(k\) increase, decrease, or stay the same when: (a) You increase the temperature (explain your choice fully). (b) You add a catalyst (explain your choice fully).

Suppose you increase the temperature of a reaction from \(100^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) and the reaction gets three times as fast. (a) Would the rate constant for the reaction at \(100^{\circ} \mathrm{C}\) be equal to the rate constant for the reaction at \(200^{\circ} \mathrm{C}\) ? (b) Suppose you took a ratio \(k_{200^{\circ} \mathrm{C}} / k_{100^{\circ} \mathrm{C}}\). According to the information given in part (a), what would you expect the value of this ratio to be?

The rate of a reaction depends both on inherent factors and on concentration. The rate constant \(k\) is associated with the inherent factors. What are they?

A student says that an exothermic reaction will always have a larger rate constant \(k\) than an endothermic one and will thus always be faster. What is wrong with her line of reasoning?

Given the general form of the rate law, Rate \(=k[\operatorname{Reactant} 1]^{x}[\text { Reactant } 2]^{y}\) answer the following questions: (a) Which part of the rate law reflects the inherent factors of the reaction? (b) What is the general name for the exponents \(x\) and \(y ?\) (c) How do we calculate the overall order of a chemical reaction? (d) Suppose the reaction is second-order with respect to reactant 1 and first- order with respect to reactant \(2 .\) What are the values of \(x\) and \(y\), and what is the overall order of a reaction with only these two reactants? (e) Suppose reactant 1 does not appear in the rate law. What does this say about the value of its order? What is the meaning of the value of its order?

True or false? (a) The orders \(x\) and \(y\) in a rate law are written directly from the balancing coefficients from the balanced equation for a reaction. (b) The overall order of a reaction is the sum of the individual orders of the reactants. (c) If you start a reaction with just reactants (no product present), then the rate of the reaction will remain constant with time. (d) If you start a reaction with just reactants (no product present), then the rate of the reaction will decrease with time.

How do we go about determining the orders in an experimental rate law? Use the term "kinetics experiments" in your answer, defining what those are.

If a reaction rate has a first-order dependence on a given reactant concentration, what will happen to the rate when the concentration of that reactant is doubled?

If a reaction rate has a second-order dependence on a given reactant concentration, what will happen to the rate when the concentration of that reactant is doubled?

The reaction \(\mathrm{A}+2 \mathrm{~B}+\mathrm{C} \rightarrow \mathrm{AB}_{2} \mathrm{C}\) has a rate that does not change when more \(C\) is added to the reaction flask. Suppose the overall reaction order is 2, and the reaction is first-order with respect to \(\mathrm{A}\). (a) Write the rate law for this reaction, (b) What is the order for reactant \(C ?\)

A reaction \(\mathrm{A}+\mathrm{B} \rightarrow\) Product is run in a balloon. (Both A and B are gases.) The balloon has a volume of 1 L and is initially loaded with 1 mole of \(\mathrm{A}\) and \(1 \mathrm{~mole}\) of \(\mathrm{B}\). The reaction has the rate law Rate \(=k[\mathrm{~A}]\) The reaction is run again using the same amount of reactants, but this time in a balloon that has a volume of \(0.5 \mathrm{~L}\). How much faster will the reaction proceed in the smaller balloon? Explain your answer.

Given the rate data below from a series of kinetics experiments, determine the orders for the following reaction, and state the overall order of the reaction: \(\mathrm{H}_{2} \mathrm{O}_{2}(a q)+3 \mathrm{I}^{-}(a q)+2 \mathrm{H}^{+}(a q) \rightarrow \mathrm{I}_{3}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)\) $$\begin{array}{cccc} \text { Experiment }\left[\mathbf{H}_{2} \mathrm{O}_{2}\right] & {\left[\mathbf{I}^{-}\right]} & {\left[\mathbf{H}^{+}\right]} & \text {Rate }(\mathbf{M} / \mathbf{s}) \\ \hline 1 & 0.010 \mathrm{M} & 0.010 \mathrm{M} & 0.00050 \mathrm{M} & 1.15 \times 10^{-6} \\ 2 & 0.020 \mathrm{M} & 0.010 \mathrm{M} & 0.00050 \mathrm{M} & 2.30 \times 10^{-6} \\ 3 & 0.010 \mathrm{M} & 0.020 \mathrm{M} & 0.00050 \mathrm{M} & 2.30 \times 10^{-6} \\ 4 & 0.010 \mathrm{M} & 0.010 \mathrm{M} & 0.00100 \mathrm{M} & 1.15 \times 10^{-6} \end{array}$$

In a kinetic study of the reaction \(2 \mathrm{~A}(g)+\mathrm{B}(g) \rightarrow \mathrm{P}(g)\) the following rate data were obtained. Write the rate law with proper orders. Give the overall order of the reaction. Finally, state what this problem confirms about the relationship between reactant orders and coefficients in the balanced equation. $$\begin{array}{cccc} & & & \begin{array}{l} \text { Rate of } \\ \text { disappearance } \end{array} \\ \text { Experiment } & {[\mathbf{A}]} & {[\mathrm{B}]} & \text { of A }(\mathrm{M} / \mathrm{s}) \\ \hline 1 & 0.0125 \mathrm{M} & 0.0253 \mathrm{M} & 0.0281 \\ 2 & 0.0250 \mathrm{M} & 0.0253 \mathrm{M} & 0.0562 \\ 3 & 0.0125 \mathrm{M} & 0.0506 \mathrm{M} & 0.1124 \end{array}$$

In a kinetic study of the reaction \(2 \mathrm{ClO}_{2}(a q)+2 \mathrm{OH}^{-}(a q) \rightarrow\) \(\mathrm{ClO}_{3}^{-}(a q)+\mathrm{ClO}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) the following rate data were obtained. Write a rate law complete with proper values for the orders. What is the overall order of the reaction? $$\begin{array}{cccc} \text { Experiment } & {\left[\mathrm{ClO}_{2}\right]} & {\left[\mathrm{OH}^{-}\right]} & \text {Rate }(\mathbf{M} / \mathrm{s}) \\ \hline 1 & 0.060 \mathrm{M} & 0.030 \mathrm{M} & 0.02484 \\ 2 & 0.020 \mathrm{M} & 0.030 \mathrm{M} & 0.00276 \\ 3 & 0.020 \mathrm{M} & 0.090 \mathrm{M} & 0.00828 \end{array}$$

Which of the following will slow down a chemical reaction? (a) Increase concentration of reactants. (b) Add catalyst. (c) Decrease temperature. (d) All of the above.

The rate constant \(k\) of a chemical reaction can be changed by (a) Changing the temperature at which the reaction is run (b) Changing the concentration of reactants (c) Adding a catalyst (d) All of the above (e) Only (a) and (c)

The mechanism for the endothermic reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}+\mathrm{X}\) is Step \(1: \mathrm{A}+\mathrm{A} \rightarrow \mathrm{C}+\mathrm{D}(\mathrm{slow})\) Step \(2: \mathrm{B}+\mathrm{D} \rightarrow \mathrm{X}+\mathrm{A}\) (fast) (a) Draw the reaction-energy profile for this reaction and label reactants, products, reaction intermediates, transition states, activation energies, and \(\Delta E_{\mathrm{rxn}} .\) (Hint: First draw a profile for step \(1 .\) Make it a very endothermic reaction, and remember that a slow reaction has a large value for \(E_{\mathrm{a}}\) Then draw a profile for step 2, using the line representing the step 1 products as the reactants line for step \(2 .\) Remember that a fast reaction has a small value for \(E_{\mathrm{a}}\). (b) What is the rate law for this reaction? (c) If you wanted to quadruple the rate of this reaction, by what factor would you have to increase the concentration of \(\mathrm{A}\) ?

In each reaction, indicate which bonds are broken and which bonds are formed: (a) \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}\) (b) \(\mathrm{PCl}_{5} \rightarrow \mathrm{PCl}_{3}+\mathrm{Cl}_{2}\) (c) \(\mathrm{H}_{2}+2 \mathrm{ICl} \rightarrow 2 \mathrm{HCl}+\mathrm{I}_{2}\) (d) \(4 \mathrm{HBr}+\mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+2 \mathrm{Br}_{2}\)

Indicate whether each reaction is endothermic or exothermic: (a) \(\mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CH}_{4}+2 \mathrm{O}_{2} \Delta E_{\mathrm{rxn}}=+890 \mathrm{~kJ}\) (b) \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \Delta E_{\mathrm{rxn}}=-890 \mathrm{~kJ}\) (c) \(\mathrm{S}+\mathrm{O}_{2} \rightarrow \mathrm{SO}_{2}+\) Heat (d) \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3} \Delta E_{\mathrm{rxn}}=-92 \mathrm{~kJ}\) (e) Heat \(+\mathrm{NH}_{4} \mathrm{NO}_{3} \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)\) (f) \(2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O} \Delta E_{\mathrm{rxn}}=-479 \mathrm{~kJ}\)

When a chemical reaction is in the ______________, the reactant bonds are just ready to break and the product bonds are just ready to form.

Determine the value of \(k\) for a reaction for which: (a) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.42\) and the fraction of collisions having the proper orientation is \(0.15\). (b) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.42\) and the fraction of collisions having the proper orientation is \(0.30\). (c) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.84\) and the fraction of collisions having the proper orientation is \(0.15\). (d) The fraction of collisions having energy \(>E_{\mathrm{a}}\) is \(0.84\) and the fraction of collisions having the proper orientation is \(0.30\).

The rate law for the reaction \(2 \mathrm{NO}+\mathrm{Br}_{2} \rightarrow 2 \mathrm{NOBr}\) is Rate \(=k[\mathrm{NO}]^{2}\left[\mathrm{Br}_{2}\right] .\) How will the rate change when: (a) [NO] is doubled? (b) \(\left[\mathrm{Br}_{2}\right]\) is tripled? (c) [NO] is tripled? (d) \(\left[\mathrm{Br}_{2}\right]\) is quadrupled? (e) [NO] is doubled and \(\left[\mathrm{Br}_{2}\right]\) is tripled?

The slowest step in a reaction mechanism is called the _______-_______ step.

The experimental rate law for the reaction \(\mathrm{A}+\mathrm{A} \rightarrow \mathrm{A}_{2}\) is Rate \(=k[\mathrm{~A}][\mathrm{BC}]\) Two mechanisms have been proposed for the reaction: Step 1: \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{AB}\) (slow) Step \(2: \mathrm{AB}+\mathrm{A} \rightarrow \mathrm{A}_{2}+\mathrm{B}\) (fast) and Step \(1: \mathrm{A}+\mathrm{BC} \rightarrow \mathrm{AB}+\mathrm{C}\) (slow) Step \(2: \mathrm{A}+\mathrm{AB} \rightarrow \mathrm{B}+\mathrm{A}_{2}\) (fast) Step \(3: \mathrm{B}+\mathrm{C} \rightarrow \mathrm{BC}\) (fast) (a) Show that each mechanism results in the correct overall reaction. (b) Which mechanism is consistent with the rate law? (c) Why does \(\mathrm{BC}\) appear in the rate law but not in the overall reaction?

For a reaction mechanism to be valid, the _______ rate law must agree with the _______ rate law.

\(\Delta E_{\mathrm{rxn}}\) for the reaction \(\mathrm{X} \rightarrow \mathrm{Y}\) is \(+30 \mathrm{~kJ}\). (a) Is the reaction endothermic or exothermic? (b) Rewrite the reaction showing heat as either a reactant or a product. (c) What is the value of \(\Delta E_{\mathrm{rxn}}\) for the reverse reaction \(\mathrm{Y} \rightarrow \mathrm{X} ?\) (d) Is the reverse reaction endothermic or exothermic? (e) Will the container in which the forward reaction \(\mathrm{X} \rightarrow\) Y occurs feel hot or cold to the touch? Why?

Determine the value of \(E_{\mathrm{a}}\) and \(\Delta E_{\mathrm{rxn}}\) for each case below. Also indicate whether each reaction is endothermic or exothermic. $$\begin{array}{lccc} & \begin{array}{l} \text { Energy of } \\ \text { reactants, kJ } \end{array} & \begin{array}{l} \text { Energy of } \\ \text { transition state, kJ } \end{array} & \begin{array}{l} \text { Energy of } \\ \text { products, kJ } \end{array} \\ \hline \text { (a) } & 100 & 150 & 130 \\ \text { (b) } & 100 & 150 & 70 \\ \text { (c) } & 50 & 175 & 130 \\ \text { (d) } & 20 & 40 & 10 \\ \hline \end{array}$$

The reaction \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}\) is exothermic. Draw a reaction-energy profile for the reaction. Label the gap that represents \(\Delta E_{\mathrm{rxn}} .\)

True or false? A catalyst in a reaction decreases the energy gap between reactants and products. If the statement is false, explain why.

Which of the following are substitution reactions: (a) \(\mathrm{CH}_{3} \mathrm{Br}+\mathrm{I}^{-} \rightarrow \mathrm{CH}_{3} \mathrm{I}+\mathrm{Br}^{-}\) (b) \(\mathrm{H}_{2}+\mathrm{Br}_{2} \rightarrow 2 \mathrm{HBr}\) (c) \(\mathrm{CH}_{2}=\mathrm{CH}_{2}+\mathrm{H}_{2} \rightarrow \mathrm{CH}_{3}-\mathrm{CH}_{3}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}+\mathrm{OH}^{-} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{Cl}^{-}\)

The rate law for a reaction involving \(\mathrm{A}(g)\) as the only reactant is: Rate \(=k[\mathrm{~A}]^{2}\) What happens to the rate when: (a) The volume of the reaction container is halved? (b) The concentration of \(\mathrm{A}\) is tripled?

The mechanism for the reaction of \(A_{2}\) with \(B\) is: Step \(1: \mathrm{A}_{2}+\mathrm{Y} \rightarrow \mathrm{AY}+\mathrm{A}\) (slow) Step \(2: \mathrm{A}+\mathrm{B} \rightarrow \mathrm{AB}\) (fast) Step 3: \(\mathrm{AY}+\mathrm{AB} \rightarrow \mathrm{Y}+\mathrm{A}_{2} \mathrm{~B}\) (fast) (a) Write the overall reaction that is occurring. (b) Which step determines the rate law for the reaction? (c) Write the rate law for the reaction. (d) What happens to the rate of the reaction when \(\left[\mathrm{A}_{2}\right]\) is doubled? (e) Which species is the catalyst? (f) Which species are reaction intermediates?

Explain why this statement is false: A reaction in which weak bonds are broken and strong bonds are formed is an endothermic reaction.

Indicate whether each of the following statements is true or false. Rewrite each false statement to make it true. (a) Raising the temperature of a reaction mixture increases the number of reactant molecules that have energy equal to or greater than \(E_{\mathrm{a}}\) (b) Lowering the temperature of a reaction mixture speeds up the reaction. (c) The rate of a reaction depends only on the number of collisions per unit time having energy equal to or greater than \(E_{\mathrm{a}}\) (d) A reaction with an orientation factor of 1 means that all reacting molecules are oriented properly.

Which reaction occurs fastest, one with \(E_{\mathrm{a}}=20 \mathrm{~kJ}\), one with \(E_{\mathrm{a}}=50 \mathrm{~kJ}\), or one with \(E_{\mathrm{a}}=75 \mathrm{~kJ}\) ?

A student says to you, "Catalysts are not used up in chemical reactions because they are not involved in the reactions." Is this statement true or false? Why?

Explain the difference between a reaction intermediate and a catalyst in terms of the order in which each appears in the various steps of a reaction mechanism.

Explain the difference between the energy factor and the orientation factor in the equation for reaction rate (Equation 13.1).

Write the general rate law for each reaction, using \(x\) and \(y\) exponents as orders: (a) \(2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}\) (b) \(2 \mathrm{H}_{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}\)

Chemical companies invest a considerable amount of time and energy in search of better catalysts for their chemical processes. Explain how this investment might pay off.

A reaction releases \(900 \mathrm{~kJ}\) of energy. (a) Is the reaction endothermic or exothermic? (b) Which are higher in the reaction-energy profile, reactants or products? Explain. (c) Does this reaction go uphill or downhill in energy? (d) Draw the reaction-energy profile.

Explain why the value of \(k\) gets larger as the temperature of a reaction mixture is increased.