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Chapter 14: Problem 89

Consider the reaction \(\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{D} .\) Is each of the following statements true or false? (a) The rate law for the reaction must be Rate \(=k[\mathrm{A}][\mathrm{B}] .\) (b) If the reaction is an elementary reaction, the rate law is second order. (c) If the reaction is an elementary reaction, the rate law of the reverse reaction is first order. (d) The activation energy for the reverse reaction must be greater than that for the forward reaction.

Short Answer

Expert verified
The short version of the answer is: (a) False (b) True (c) False (d) False

Step by step solution

01

(a) Checking the rate law for the reaction

: The statement says the rate law must be \(Rate = k[A][B]\). This is not necessarily true. The rate law of the reaction would depend on the reaction mechanism and would be determined experimentally. So, the provided statement is false.
02

(b) Checking if the rate law is second order for an elementary reaction

: If the given reaction is an elementary reaction, then the rate law would depend on the concentrations of the reacting species with an exponent equal to their stoichiometric coefficients. In this case, the rate law would be \(Rate = k[A][B]\). This is indeed a second-order reaction. So, the provided statement is true.
03

(c) Checking if the rate law of the reverse reaction is first order for an elementary reaction

: The reverse reaction would be \(C + D \longrightarrow A + B\). If the given reaction is an elementary reaction, then the rate law of the reverse reaction would also depend on the concentrations of the reacting species in the reverse reaction, with an exponent equal to their stoichiometric coefficients. In this case, the rate law for the reverse reaction would be \(Rate = k'[C][D]\). This is also a second-order reaction, not first order. So, the provided statement is false.
04

(d) Checking if the activation energy for the reverse reaction must be greater than that for the forward reaction

: The activation energy for the reverse reaction (\(E_{a,reverse}\)) doesn't necessarily have to always be greater than that for the forward reaction (\(E_{a,forward}\)). The relation between the activation energies would depend on the reaction and cannot be generalized. So, the provided statement is false. In summary: (a) False (b) True (c) False (d) False

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Most popular questions from this chapter

Many primary amines, RNH \(_{2},\) where \(R\) is a carbon-containing fragment such as \(C H_{3}, C H_{3} C H_{2},\) and so on, undergo reactions where the transition state is tetrahedral. (a) Draw a hybrid orbital picture to visualize the bonding at the nitrogen in a primary amine (just use a \(C\) atom for \(^{4} \mathrm{R}^{\prime \prime}\) . (b) What kind of reactant with a primary amine can produce a tetrahedral intermediate?

As described in Exercise 14.41 , the decomposition of sulfuryl chloride \(\left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right)\) is a first-order process. The rate constant for the decomposition at 660 \(\mathrm{K}\) is \(4.5 \times 10^{-2} \mathrm{s}^{-1}\) .half-life for this reaction? (b) If you start with 0.050\(M \mathrm{I}_{2}\) at this temperature, how much will remain after 5.12 s assuming that the iodine atoms do not recombine to form \(\mathrm{I}_{2}\) ?

Urea \(\left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right)\) is the end product in protein metabolism in animals. The decomposition of urea in 0.1 \(\mathrm{M} \mathrm{HCl}\) occurs according to the reaction $$\mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}^{+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NH}_{4}^{+}(a q)+\mathrm{HCO}_{3}^{-}(a q)$$ The reaction is first order in urea and first order overall. When \(\left[\mathrm{NH}_{2} \mathrm{CONH}_{2}\right]=0.200 M,\) the rate at \(61.05^{\circ} \mathrm{C}\) is \(8.56 \times 10^{-5} \mathrm{M} / \mathrm{s}\) , (a) What is the rate constant, \(k ?\) units of \(s^{-1}\) . (c) Calculate the half-life of the reaction. (d) How long does it take for the absorbance to fall to 0.100\(?\)

The activation energy of an uncatalyzed reaction is 95 \(\mathrm{kJ} / \mathrm{mol} .\) The addition of a catalyst lowers the activation energy to 55 \(\mathrm{kJ} / \mathrm{mol}\) . Assuming that the collision factor remains the same, by what factor will the catalyst increase the rate of the reaction at (a) \(25^{\circ} \mathrm{C},\) (b) \(125^{\circ} \mathrm{C} ?\)

(a) Most commercial heterogeneous catalysts are extremely finely divided solid materials. Why is particle size important? (b) What role does adsorption play in the action of a heterogeneous catalyst?
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