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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 (option b) and the temperature (option c). The concentration of the reactants (option a) and the order of the reaction (option d) do not affect the rate constant.

Step by step solution

01

Option a: the concentration of the reactants

The rate constant does not depend on the concentration of the reactants. The rate constant best describes the inherent speed of a reaction, and while the overall reaction rate is affected by the concentration, the rate constant remains constant for a specific reaction at a specific temperature. So, this option is incorrect.
02

Option b: the nature of the reactants

The nature of the reactants plays a significant role in determining the rate constant. Different reactants have their own distinct reactivity depending on their molecular structure, bonding, and other factors. A reaction with more reactive species would have a higher rate constant. Therefore, this option is correct.
03

Option c: the temperature

Temperature affects the rate constant through the Arrhenius equation, which states that the rate constant is proportional to the exponential of the activation energy divided by the product of the gas constant and the temperature: \[k = A\exp\left(-\frac{E_a}{R}\cdot \frac{1}{T}\right)\] where \(A\) is the pre-exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. As the temperature increases, the rate constant increases as well, and vice versa. Therefore, this option is correct.
04

Option d: the order of the reaction

The order of the reaction (n) indicates how the rate of the reaction depends on the concentration of the reactants: \[\text{rate} = k[\text{reactants}]^n\] The rate constant itself does not depend on the order of the reaction. It is simply a proportionality constant that links the concentration of the reactants to the rate of the reaction. Therefore, this option is incorrect. To summarize, the rate constant depends on the nature of the reactants (option b) and the temperature (option c).

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Most popular questions from this chapter

The reaction $$ \left(\mathrm{CH}_{3}\right)_{3} \mathrm{CBr}+\mathrm{OH}^{-} \longrightarrow\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}+\mathrm{Br}^{-} $$ 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. 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 \(25^{\circ} \mathrm{C}\) .

Rate Laws from Experimental Data: Initial Rates Method. The reaction $$2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{NOCl}(g)$$ was studied at \(-10^{\circ} \mathrm{C}\). The following results were obtained where $$\text { Rate }=-\frac{\Delta\left[\mathrm{Cl}_{2}\right]}{\Delta t}$$ $$ \begin{array}{ccc} {[\mathrm{NO}]_{0}} & {\left[\mathrm{Cl}_{2}\right]_{0}} & \text { Initial Rate } \\ (\mathrm{mol} / \mathrm{L}) & (\mathrm{mol} / \mathrm{L}) & (\mathrm{mol} / \mathrm{L} \cdot \mathrm{min}) \\ 0.10 & 0.10 & 0.18 \\ 0.10 & 0.20 & 0.36 \\ 0.20 & 0.20 & 1.45 \end{array} $$ a. What is the rate law? b. What is the value of the rate constant?

In the Haber process for the production of ammonia, $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ what is the relationship between the rate of production of ammonia and the rate of consumption of hydrogen?

A certain reaction has the following general form: $$ \mathrm{aA} \longrightarrow \mathrm{bB} $$ At a particular temperature and \([\mathrm{A}]_{0}=2.80 \times 10^{-3} M,\) con- centration versus time data were collected for this reaction, and a plot of 1\(/[\mathrm{A}]\) versus time resulted in a straight line with a slope value of \(+3.60 \times 10^{-2} \mathrm{L} / \mathrm{mol} \cdot \mathrm{s}\) . a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. Calculate the half-life for this reaction. c. How much time is required for the concentration of A to decrease to \(7.00 \times 10^{-4} M ?\)

A certain substance, initially at 0.10\(M\) in solution, decomposes by second- order kinetics. If the rate constant for this process is 0.40 \(\mathrm{L} / \mathrm{mol} \cdot \min\) , how much time is required for the concentration to reach 0.020 \(\mathrm{M}\) ?
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