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Chapter 11: 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). The nature of the reactants affects the rate constant because different reactions have different rate constants depending on the reactants involved and the mechanism of the reaction. The temperature affects the rate constant, as the reactant molecules have more kinetic energy at higher temperatures, making it more likely that they will collide with sufficient energy to overcome the activation energy barrier. This is described by the Arrhenius equation: \(k(T) = Ae^{(-Ea/RT)}\).

Step by step solution

01

Factor a: Concentration of the Reactants

The rate constant (k) is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants. However, the rate constant itself doesn't change with the concentration of the reactants. So, (a) is not a factor affecting the rate constant.
02

Factor b: Nature of the Reactants

The nature of the reactants affects the rate constant. Different reactions have different rate constants depending on the reactants involved and the mechanism of the reaction. For example, reactions involving ionic species usually have larger rate constants compared to those involving covalent species. So, (b) is a factor affecting the rate constant.
03

Factor c: Temperature

The temperature affects the rate constant. As the temperature increases, the rate constant increases as well, because the reactant molecules have more kinetic energy, making it more likely that they will collide with sufficient energy to overcome the activation energy barrier. This is described by the Arrhenius equation: \[k(T) = Ae^{(-Ea/RT)}\] where \(k(T)\) = rate constant at temperature T, A = pre-exponential factor, Ea = activation energy, R = gas constant, and T = temperature in Kelvin. So, (c) is a factor affecting the rate constant.
04

Factor d: Order of the Reaction

The order of the reaction affects the relationship between the rate of the reaction and the concentrations of the reactants, but it doesn't affect the rate constant itself. The rate constant is the proportionality constant in the rate law expression, and its value remains the same for a given reaction at a fixed temperature, regardless of the order of the reaction. So, (d) is not a factor affecting the rate constant. In conclusion, 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

The activation energy for some reaction $$\mathrm{X}_{2}(g)+\mathrm{Y}_{2}(g) \longrightarrow 2 \mathrm{XY}(g)$$ is \(167 \mathrm{kJ} / \mathrm{mol},\) and \(\Delta E\) for the reaction is \(+28 \mathrm{kJ} / \mathrm{mol} .\) What is the activation energy for the decomposition of XY?

For the reaction \(\mathrm{A} \rightarrow\) products, successive half-lives are observed to be \(10.0,20.0,\) and 40.0 min for an experiment in which \([\mathrm{A}]_{0}=0.10 \mathrm{M} .\) Calculate the concentration of \(\mathrm{A}\) at the following times. a. \(80.0 \mathrm{min}\) b. \(30.0 \mathrm{min}\)

Draw a rough sketch of the energy profile for each of the following cases: a. \(\Delta E=+10 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=25 \mathrm{kJ} / \mathrm{mol}\) b. \(\Delta E=-10 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{kJ} / \mathrm{mol}\) c. \(\Delta E=-50 \mathrm{kJ} / \mathrm{mol}, E_{\mathrm{a}}=50 \mathrm{kJ} / \mathrm{mol}\)

Each of the statements given below is false. Explain why. a. The activation energy of a reaction depends on the overall energy change \((\Delta E)\) for the reaction. b. The rate law for a reaction can be deduced from examination of the overall balanced equation for the reaction. c. Most reactions occur by one-step mechanisms.

A proposed mechanism for a reaction is $$\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Br} \longrightarrow \mathrm{C}_{4} \mathrm{H}_{9}^{+}+\mathrm{Br}^{-} \quad \text { Slow }$$ $$\mathrm{C}_{4} \mathrm{H}_{9}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}_{2}^{+} \quad \text { Fast }$$ $$\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}_{2}^{+}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}+\mathrm{H}_{3} \mathrm{O}^{+}\quad \text { Fast }$$ Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction? What are the intermediates in the proposed mechanism?
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