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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 nature of the reactants influences the value of \(k\) through factors like reactant particle size, chemical bonds, and their physical state. The rate constant also depends on temperature, as an increase in temperature leads to an increase in the rate of the reaction, which can be modeled using the Arrhenius equation: \(k=Ae^{-\frac{E_a}{RT}}\).

Step by step solution

01

Option a: concentration of reactants

The rate constant \((k)\) does not depend on the concentration of reactants. In fact, the rate constant is used alongside the concentration of the reactants to calculate the rate of reaction. If the concentration changes, the rate of reaction will change accordingly, but the rate constant remains the same at a constant temperature.
02

Option b: nature of reactants

The rate constant \((k)\) depends on the nature of the reactants. Different reactions have different rates of reactions, which depend on the physical and chemical properties of the reactants being used. Factors like the size of the reactant particles, their chemical bonds, and whether they are in a solid, liquid, or gaseous state all influence the value of \(k\).
03

Option c: temperature

The rate constant \((k)\) depends on temperature. When the temperature increases, the kinetic energy of particles increases, and more collisions between reactants occur with sufficient energy to overcome the activation energy barrier. As a result, the rate of the reaction increases and so does the rate constant. According to the Arrhenius equation, the relation between the rate constant and temperature can be modeled as \(k=Ae^{-\frac{E_a}{RT}}\), 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.
04

Option d: order of the reaction

The rate constant \((k)\) does not directly depend on the order of the reaction. The order of the reaction is the sum of the exponents in the reactants to which they are raised in the rate law. The order of a reaction and the rate constant are two separate parameters that describe the reaction. However, the units of the rate constant depend on the order of the reaction. For example, the units of a first-order reaction rate constant are s⁻¹ (inverse seconds), while the units of a second-order reaction rate constant are M⁻¹s⁻¹ (inverse molarity per second). In conclusion, the rate constant \((k)\) depends on options b: the nature of the reactants, and c: the temperature.

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Most popular questions from this chapter

Describe at least two experiments you could perform to determine a rate law.

One of the concerns about the use of Freons is that they will migrate to the upper atmosphere, where chlorine atoms can be generated by the following reaction: $$ \mathrm{CCl}_{2} \mathrm{~F}_{2} \stackrel{\mathrm{hv}}{\longrightarrow} \mathrm{CF}_{2} \mathrm{Cl}+\mathrm{Cl} $$ Chlorine atoms can act as a catalyst for the destruction of ozone. The activation energy for the reaction $$ \mathrm{Cl}+\mathrm{O}_{3} \longrightarrow \mathrm{ClO}+\mathrm{O}_{2} $$ is \(2.1 \mathrm{~kJ} / \mathrm{mol}\). Which is the more effective catalyst for the destruction of ozone, \(\mathrm{Cl}\) or \(\mathrm{NO}\) ? (See Exercise \(69 .\) )

Consider the reaction $$ 3 \mathrm{~A}+\mathrm{B}+\mathrm{C} \longrightarrow \mathrm{D}+\mathrm{E} $$ where the rate law is defined as $$ -\frac{\Delta[\mathrm{A}]}{\Delta t}=k[\mathrm{~A}]^{2}[\mathrm{~B}][\mathrm{C}] $$ An experiment is carried out where \([\mathrm{B}]_{0}=[\mathrm{C}]_{0}=1.00 \mathrm{M}\) and \([\mathrm{A}]_{0}=1.00 \times 10^{-4} M\) a. If after \(3.00 \mathrm{~min},[\mathrm{~A}]=3.26 \times 10^{-5} M\), calculate the value of \(k\). b. Calculate the half-life for this experiment. c. Calculate the concentration of \(\mathrm{B}\) and the concentration of \(\mathrm{A}\) after \(10.0 \mathrm{~min}\).

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.

A certain reaction has the following general form: \(\mathrm{aA} \longrightarrow \mathrm{bB}\) At a particular temperature and \([\mathrm{A}]_{0}=2.00 \times 10^{-2} M\), concentration versus time data were collected for this reaction, and a plot of \(\ln [\mathrm{A}]\) versus time resulted in a straight line with a slope value of \(-2.97 \times 10^{-2} \mathrm{~min}^{-1}\). 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 \(\mathrm{A}\) to decrease to \(2.50 \times 10^{-3} M ?\)
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