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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 decomposition of ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\( on an alumina \)\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)$ surface $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ was studied at 600 \(\mathrm{K}\) . Concentration versus time data were collected for this reaction, and a plot of [A] versus time resulted in a straight line with a slope of $-4.00 \times 10^{-5} \mathrm{mol} / \mathrm{L} \cdot \mathrm{s}$ . a. Determine the rate law, the integrated rate law, and the value of the rate constant for this reaction. b. If the initial concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) was \(1.25 \times 10^{-2} M\) calculate the half-life for this reaction. c. How much time is required for all the \(1.25 \times 10^{-2} \mathrm{M}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) to decompose?

Which of the following statement(s) is(are) true? a. The half-life for a zero-order reaction increases as the reaction proceeds. b. A catalyst does not change the value of \(\Delta \mathrm{E}\) . c. The half-life for a reaction, aA \(\longrightarrow\) products, that is first order in A increases with increasing \([\mathrm{A}]_{0} .\) d. The half-life for a second-order reaction increases as the reaction proceeds.

Two isomers (A and B) of a given compound dimerize as follows: $$ \begin{array}{l}{2 \mathrm{A} \stackrel{k_{1}}{\longrightarrow} A_{2}} \\ {2 \mathrm{B} \stackrel{k_{2}}{\longrightarrow} \mathrm{B}_{2}}\end{array} $$ Both processes are known to be second order in reactant, and \(k_{1}\) is known to be 0.250 \(\mathrm{L} / \mathrm{mol} \cdot \mathrm{s}\) at $25^{\circ} \mathrm{C}\( . In a particular experiment \)\mathrm{A}\( and \)\mathrm{B}$ were placed in separate containers at \(25^{\circ} \mathrm{C},\) where \([\mathrm{A}]_{0}=1.00 \times 10^{-2} M\) and $[\mathrm{B}]_{0}=2.50 \times 10^{-2} M\( It was found that after each reaction had progressed for \)3.00 \mathrm{min},[\mathrm{A}]=3.00[\mathrm{B}]$ . In this case the rate laws are defined as $$ \begin{array}{l}{\text { Rate }=-\frac{\Delta[\mathrm{A}]}{\Delta t}=k_{1}[\mathrm{A}]^{2}} \\ {\text { Rate }=-\frac{\Delta[\mathrm{B}]}{\Delta t}=k_{2}[\mathrm{B}]^{2}}\end{array} $$ a. Calculate the concentration of \(\mathrm{A}_{2}\) after 3.00 \(\mathrm{min}\) . b. Calculate the value of \(k_{2}\) . c. Calculate the half-life for the experiment involving A.

The combustion of carbohydrates and the combustion of fats are both exothermic processes, yet the combustion of carbohydrates is a faster process. How can this be?

Consider the general reaction $$ \mathrm{aA}+\mathrm{bB} \longrightarrow \mathrm{cC} $$ and the following average rate data over some time period \(\Delta t :\) $$ \begin{aligned}-\frac{\Delta \mathrm{A}}{\Delta t} &=0.0080 \mathrm{mol} / \mathrm{L} \cdot \mathrm{s} \\\\-& \frac{\Delta \mathrm{B}}{\Delta t}=0.0120 \mathrm{mol} / \mathrm{L} \cdot \mathrm{s} \\ \frac{\Delta \mathrm{C}}{\Delta t} &=0.0160 \mathrm{mol} / \mathrm{L} \cdot \mathrm{s} \end{aligned} $$ Determine a set of possible coefficients to balance this general reaction.
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