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Chapter 12: Problem 9

The rate constant \((k)\) depends on which of the following (there may be more than one answer)? a. the concentration of the reactants b. the nature of the reactants c. the temperature d. the order of the reaction Explain.

Short Answer

Expert verified
The rate constant \((k)\) depends on the nature of the reactants (b) and the temperature (c). Different reactants have different activation energies, collision frequencies, and orientations, which influence the rate constant. Temperature also affects the rate constant, as higher temperatures increase the kinetic energy and collision frequency, making it more likely for molecules to overcome the activation energy barrier.

Step by step solution

01

Understanding Rate Constant

The rate constant \((k)\) is a part of the rate law equation which describes the relationship between the rate of a reaction and the concentrations of reactants. It provides insights into the speed of a reaction, and its value depends on various factors.
02

a. Concentration of the Reactants

The rate constant \((k)\) does not depend on the concentration of the reactants. This is because, in the rate law equation, the rate constant is part of a mathematical product with the concentrations of the reactants raised to some powers, to provide the overall rate of the reaction. Therefore, the rate constant itself remains constant.
03

b. Nature of the Reactants

The rate constant \((k)\) is influenced by the nature of the reactants. Different reactants will have different intermolecular and intramolecular forces, which affect the activation energies, collision frequencies, and orientations of the molecules during the reaction. As a result, the rate constant may differ for reactions involving different reactants.
04

c. Temperature

The rate constant \((k)\) is influenced by temperature. According to the Arrhenius equation, as temperature increases, the rate constant also increases. This is due to the fact that at higher temperatures, the molecules have increased kinetic energy, which in turn increases collision frequency and the probability of overcoming the activation energy barrier to react.
05

d. Order of the Reaction

The rate constant \((k)\) does not "depend" on the order of the reaction in a direct sense, but it varies for reactions of different orders under the same conditions. For example, increasing the order of a reaction generally results in a higher rate constant. So while the variation of the rate constant is related to the order of the reaction, it is not a direct impact or dependency. To summarize, out of the four options provided, the rate constant \((k)\) depends on the nature of the reactants (b) and the temperature (c).

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Most popular questions from this chapter

A certain substance, initially present at \(0.0800 M\), decomposes by zero-order kinetics with a rate constant of \(2.50 \times 10^{-2}\) \(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}\). Calculate the time (in seconds) required for the system to reach a concentration of \(0.0210 \mathrm{M}\).

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The reaction $$ \left(\mathrm{CH}_{\mathrm{3}}\right)_{3} \mathrm{CBr}+\mathrm{OH}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}+\mathrm{Br}^{-} $$ in a certain solvent is first order with respect to \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}\) and zero order with respect to \(\mathrm{OH}^{-}\). In several experiments, the rate constant \(k\) was determined at different temperatures. \(\mathrm{A}\) plot of \(\ln (k)\) versus \(1 / T\) was constructed resulting in a straight line with a slope value of \(-1.10 \times 10^{4} \mathrm{~K}\) and \(y\) -intercept of 33.5. Assume \(k\) has units of \(\mathrm{s}^{-1}\). a. Determine the activation energy for this reaction. b. Determine the value of the frequency factor \(A\). c. Calculate the value of \(k\) at \(25^{\circ} \mathrm{C}\).
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