Chapter 13

A reaction is endothermic by \(65 \mathrm{~kJ} / \mathrm{mol}\) (that is, \(\Delta E_{\mathrm{rxn}}=+65 \mathrm{~kJ}\) for every mole of product formed). (a) Draw a reaction-energy profile for this reaction, assuming the energy of the reactants to be \(100 \mathrm{~kJ} / \mathrm{mol}\). (b) Does this reaction go uphill or downhill in energy? (c) What is the value of \(\Delta E_{\mathrm{rxn}} ?\) (d) Will the container in which this reaction is carried out feel hot or cold to the touch? Explain.

A reaction has a \(\Delta E_{\mathrm{rxn}}\) of \(-450 \mathrm{~kJ} / \mathrm{mol}\). The products have an energy of \(20 \mathrm{~kJ} / \mathrm{mol}\). (a) Is the energy of the reactants higher or lower than that of the products? Explain. (b) What is the energy of the reactants? (c) Is the reaction exothermic or endothermic? How do you know? (d) Does the reaction go uphill or downhill in energy? (e) Draw a reaction-energy profile for the reaction.

The energy released by the reaction \(\mathrm{A} \rightarrow \mathrm{B}\) is \(400 \mathrm{~kJ} / \mathrm{mol}\). (a) What is \(\Delta E_{\text {forward } \mathrm{rxn}}\) ? (b) What is \(\Delta E_{\text {reverse rxn }}\) ?

As the reaction \(\mathrm{A} \rightarrow \mathrm{B}\) proceeds, the container in which it is run feels cold to the touch. Measurements show a net energy change of \(250 \mathrm{~kJ} / \mathrm{mol}\). (a) What is \(\Delta E_{\text {forward rxn }}\) ? (b) What is \(\Delta E_{\text {reverse rxn }}\) ?

As the reaction \(\mathrm{A} \rightarrow \mathrm{B}\) proceeds, the container in which it is run feels hot to the touch. Measurements show a net energy change of \(250 \mathrm{~kJ} / \mathrm{mol}\). (a) What is \(\Delta E_{\text {forward rxn }}\) ? (b) What is \(\Delta E_{\text {reverse rxn }}\) ?

Consider the hydrogen combustion reaction, where \(\Delta E_{\mathrm{rxn}}=-479 \mathrm{~kJ} .\) If the energy absorbed in breaking the reactant bonds is \(1370 \mathrm{~kJ}\), how much energy is released as the product bonds form?

Consider the reaction \(\Lambda_{2}+\mathrm{B}_{2} \rightarrow 2 \Lambda \mathrm{B}\). Breaking \(1 \mathrm{molc}\) of \(\Lambda-\Lambda\) bonds and \(1 \mathrm{molc}\) of \(\mathrm{B}-\mathrm{B}\) bonds requires \(2200 \mathrm{~kJ}\). Forming 1 mole of \(\mathrm{A}-\mathrm{B}\) bonds releases \(1000 \mathrm{~kJ}\). (a) Is this reaction exothermic or endothermic? Explain. (b) What is the value of \(\Delta E_{\mathrm{rxn}} ?\) (Get the sign right.) How is it to be interpreted?

Consider the reaction \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB}\), for which \(\Delta E_{\mathrm{rxn}}=-100 \mathrm{~kJ}\). Forming 1 mole of A \(-B\) bonds releases \(150 \mathrm{~kJ}\). How much energy does it take to break the reactant bonds?

Draw two reaction-energy profiles, one for an endothermic reaction A and one for an exothermic reaction B. Make the profile for reaction A represent a faster reaction than reaction \(\mathrm{B}\) by drawing the two \(E_{a}\) barriers to scale.

Draw two reaction-energy profiles, one for an endothermic reaction \(\mathrm{A}\) and one for an exothermic reaction B. Make the profile for B represent the faster reaction by drawing the two \(E_{\mathrm{a}}\) barriers to scale.

Consider our substitution reaction between \(\mathrm{OH}^{-}\) and \(\mathrm{CH}_{3} \mathrm{Br}\). Imagine it is occurring in a solution where there are 1000 collisions every second between \(\mathrm{OH}^{-}\) ions and \(\mathrm{CH}_{3}\) Br molecules. Suppose only \(10 \%\) of these collisions are sufficiently energetic to lead to products. Also, assume that the orientation factor is \(0.2\). (a) What does an orientation factor of \(0.2\) mean? (b) What is the rate of this reaction? Give your answer in number of \(\mathrm{CH}_{3} \mathrm{OH}\) molecules formed per second.

Write a general rate law for the reaction $$2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}$$ using \(x\) and \(y\) as orders.

Write a general rate law for the reaction $$\mathrm{H}_{2} \mathrm{O}_{2}(a q)+3 \mathrm{I}^{-}(a q)+2 \mathrm{H}^{+}(a q) \rightarrow \mathrm{I}_{3}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ using \(x, y, z\) as orders.

Why should the number of collisions per second between reactant molecules have anything to do with their concentration?

For the reaction $$\mathrm{BrO}_{3}^{-}+5 \mathrm{Br}^{-}+6 \mathrm{H}^{+} \rightarrow 3 \mathrm{Br}_{2}+3 \mathrm{H}_{2} \mathrm{O}$$ the experimentally determined rate law is: $$\text { Rate }=k\left[\mathrm{BrO}_{3}^{-}\right]\left[\mathrm{Br}^{-}\right]\left[\mathrm{H}^{+}\right]^{2}$$ (a) What is the order of this reaction with respect to \(\mathrm{Br}^{-}\) ? (b) What is the order of this reaction with respect to \(\mathrm{H}^{+} ?\) (c) What is the overall order of the reaction? (d) What happens to the rate of this reaction when you double the \(\mathrm{H}^{+}\) concentration?

Use the given kinetics data to write the rate law for the reaction $$2 \mathrm{NO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NO}_{2}$$ $$\begin{array}{cccc} \text { Experiment } & \text { Initial [NO] } & \text { Initial }\left[\mathrm{O}_{2}\right] & \text { Rate of } \mathrm{NO}_{2} \text { formation (M/s) } \\ \hline 1 & 0.015 \mathrm{M} & 0.015 \mathrm{M} & 0.048 \\ 2 & 0.030 \mathrm{M} & 0.015 \mathrm{M} & 0.192 \\ 3 & 0.015 \mathrm{M} & 0.030 \mathrm{M} & 0.096 \\ 4 & 0.030 \mathrm{M} & 0.030 \mathrm{M} & 0.384 \end{array}$$

Describe the following reaction in terms of which bonds must be broken and which bonds must be formed: \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}+3 \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\)

Indicate if the following reactions are examples of a substitution reaction. Explain for each. (a) \(\mathrm{CH}_{3} \mathrm{I}+\mathrm{Cl}^{-} \rightarrow \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{I}^{-}\) (b) \(\mathrm{NH}_{3}+\mathrm{CH}_{3} \mathrm{I} \rightarrow\left[\left(\mathrm{CH}_{3}\right) \mathrm{NH}_{3}\right]^{+} \mathrm{I}^{-}\)

What is meant by the mechanism of a chemical reaction?

Which branch of chemistry concerns itself with the study of reaction rates and the factors that affect rates?

Regarding a chemical reaction's mechanism: (a) Suppose we could see individual molecules as they undergo a chemical reaction. Why might it still be difficult to directly observe the reaction's mechanism? (b) What do chemist typically do to indirectly "see" a reaction mechanism?

What is one benefit of understanding a reaction's mechanism?

Compound A converts to compound \(\mathrm{B} ; \Delta E_{\mathrm{rxn}}\) is \(-100 \mathrm{~kJ} / \mathrm{mol}\). Is compound \(\mathrm{B}\) at a higher or lower energy level than compound A? By how much?

Compound A has half as much energy in it as compound \(\mathrm{B}\). If compound A converts to \(\mathrm{B}\), will this reaction release energy into the surroundings or absorb energy from the surroundings? Explain your answer.

In a chemical reaction, compound A is converted to compound \(\mathrm{B}\). In the process, energy is absorbed from the surroundings. Which compound is at a higher energy level? Explain your answer.

In a chemical reaction, compound \(C\) is converted to compound D. In the process, energy is released into the surroundings. Which compound is at a higher energy level? Explain your answer.

A reaction occurs in which 1 mole of \(\mathrm{A}\) is converted to 1 mole of \(B\). If 1 mole of \(A\) has an energy content of \(20 \mathrm{~kJ}\) and 1 mole of \(\mathrm{B}\) has an energy content of \(60 \mathrm{~kJ}\), is this reaction exothermic or endothermic? Calculate \(\Delta E_{\mathrm{rxn}} .\)

\(\Delta\) (Any quantity) is always defined as (final value of quantity) - (initial value of quantity). Now consider the quantity \(\Delta E_{\mathrm{rxn}}\). (a) For the forward reaction \(\mathrm{R} \rightarrow \mathrm{P}\), is \(\Delta E_{\mathrm{rxn}}=E_{\text {Reactants }}-E_{\text {Products }} ?\) Explain your answer. (b) According to your answer to (a), what does it mean when \(\Delta E_{\mathrm{rxn}}\) for a reaction is negative?

The reaction of Problem \(13.40\) is run in the reverse direction \((\mathrm{P} \rightarrow \mathrm{R})\). (a) Is it exothermic or endothermic? (b) Calculate \(\Delta E_{\mathrm{rxn}} .\) (c) Is what you just said and calculated for (a) and (b) consistent with the definition of \(\Delta\) (any quantity) given in Problem \(13.41\) ? Explain.

The value of \(\Delta E_{\mathrm{ryn}}\) for an exothermic reaction is always negative. (a) Why is this so in terms of \(E_{\text {reactants }}\) versus \(E_{\text {products }} ?\) (b) Why is this so in terms of bonds broken in the reactants versus bonds formed in the products?

For a particular chemical reaction, the absorbed energy is \(800 \mathrm{~kJ}\) to break old bonds, and \(400 \mathrm{~kJ}\) is released on forming new bonds. Calculate \(\Delta E_{\mathrm{rxn}}\) and comment on whether this reaction is exothermic or endothermic. Explain why.

For a particular reaction, the absorbed energy is \(800 \mathrm{~kJ}\) to break old bonds, and \(\Delta E_{\mathrm{rxn}}\) is equal to \(-800 \mathrm{~kJ}\). How much energy is released into the surroundings as the product bonds are formed?

What do we mean by activation energy?

What is the relationship between the rate of a reaction and the value of \(E_{\mathrm{a}}\) for the reaction?

True or false? An energy-downhill reaction can always be expected to be faster than an energyuphill reaction. Explain your answer.

A reaction is exothermic, with \(\Delta E_{\mathrm{rxn}}=-40 \mathrm{~kJ}\), and the transition state is \(20 \mathrm{~kJ}\) higher in energy than the reactants. Sketch a reaction-energy profile consistent with this information, complete with labels for the distances representing \(\Delta E_{\mathrm{rxn}}\) and \(E_{\mathrm{a}} .\)

Consider the transition state for a chemical reaction. (a) What is it (define it). (b) Can there be only imminent bond breaking in a transition state? Explain.

For a particular reaction, the reactants are at \(30 \mathrm{~kJ}\), the products are at \(60 \mathrm{~kJ}\), and the transition state is at \(100 \mathrm{~kJ} .\) Sketch a reactionenergy profile showing both \(\Delta E_{\mathrm{rxn}}\) and \(E_{\mathrm{a}}\). Also, calculate the value of \(\Delta E_{\mathrm{rxn}}\) and \(E_{\mathrm{a}}\), and state whether this reaction is endothermic or exothermic.

Would decreasing the size of \(E_{a}\) increase or decrease the rate of a reaction? Explain your choice fully.

Is reaction rate directly or inversely related to \(E_{a}\) ?

Would increasing the temperature increase or decrease the rate of a reaction? Explain your choice fully.

At a given temperature, what factors determine which reactant molecules can become product molecules?

Using reaction-energy profiles, plot two exothermic reactions that have the same \(\Delta E_{\mathrm{rxn}}\), but make one reaction substantially faster than the other. Label the plots "fast" and "slow," and explain why you labeled them as you did.

Reactions go faster when heated. Astudent claims this is because as temperature increases, the activation energy \(E_{\mathrm{a}}\) for a reaction decreases. Is this student correct or incorrect? If incorrect, then explain what happens to \(E_{\mathrm{a}}\) upon heating a reaction.

Why might one reaction have a much larger \(E_{a}\) than another reaction?

What is the rule of thumb for how reaction rate changes as the temperature changes?

How can the orientation of reactant molecules as they collide play a role in substitution reactions?

If there were no orientation requirement for collisions, would reactions be faster or slower than they are? Explain your answer.

What is a catalyst and why is so little catalyst needed to get the desired effect?

In general, how does a catalyst increase the rate of a chemical reaction?