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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

Hydrogen peroxide and the iodide ion react in acidic solution as follows: $$\mathrm{H}_{2} \mathrm{O}_{2}(a q)+3 \mathrm{I}^{-}(a q)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{I}_{3}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ The kinetics of this reaction were studied by following the decay of the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) and constructing plots of \(\ln \left[\mathrm{H}_{2} \mathrm{O}_{2}\right]\) versus time. All the plots were linear and all solutions had \(\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]_{0}=8.0 \times 10^{-4} \mathrm{mol} / \mathrm{L} .\) The slopes of these straight lines depended on the initial concentrations of \(\mathrm{I}^{-}\) and \(\mathrm{H}^{+} .\) The results follow: The rate law for this reaction has the form $$\text { Rate }=\frac{-\Delta\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]}{\Delta t}=\left(k_{1}+k_{2}\left[\mathrm{H}^{+}\right]\right)\left[\mathrm{I}^{-}\right]^{m}\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]^{n}$$ a. Specify the order of this reaction with respect to \(\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]\) and \(\left[\mathrm{I}^{-}\right]\) b. Calculate the values of the rate constants, \(k_{1}\) and \(k_{2}\) c. What reason could there be for the two-term dependence of the rate on \(\left[\mathrm{H}^{+}\right] ?\)

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 K. Concentration versus time data were collected for this reaction, and a plot of \([\mathrm{A}]\) 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 \(1.25 \times 10^{-2} M\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) to decompose?

The rate law for the decomposition of phosphine \(\left(\mathrm{PH}_{3}\right)\) is $$\text { Rate }=-\frac{\Delta\left[\mathrm{PH}_{3}\right]}{\Delta t}=k\left[\mathrm{PH}_{3}\right]$$ It takes \(120 .\) s for \(1.00 M\) PH \(_{3}\) to decrease to 0.250 M. How much time is required for \(2.00\space \mathrm{M} \mathrm{PH}_{3}\) to decrease to a concentration of \(0.350\space \mathrm{M} ?\)

Chemists commonly use a rule of thumb that an increase of \(10 \space\mathrm{K}\) in temperature doubles the rate of a reaction. What must the activation energy be for this statement to be true for a temperature increase from 25 to \(35^{\circ} \mathrm{C} ?\)

The rate law for the reaction $$\mathrm{Cl}_{2}(g)+\mathrm{CHCl}_{3}(g) \longrightarrow \mathrm{HCl}(g)+\mathrm{CCl}_{4}(g)$$ is $$\text { Rate }=k\left[\mathrm{Cl}_{2}\right]^{1 / 2}\left[\mathrm{CHCl}_{3}\right]$$ What are the units for \(k\), assuming time in seconds and concentration in mol/L?
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