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Chapter 14: Problem 28

Write the Arrhenius equation and define all terms.

Short Answer

Expert verified
The Arrhenius equation is given by \(k = Ae^{-Ea/RT}\), where 'k' is the rate constant, 'A' is the pre-exponential factor, 'Ea' is the activation energy, 'R' is the Universal gas constant, and 'T' is the absolute temperature.

Step by step solution

01

Write the Arrhenius Equation

Firstly, write down the Arrhenius equation itself. It is \(k = Ae^{-Ea/RT}\), in which k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and T is the temperature.
02

Define 'k'

'k' denotes the rate constant. It is the proportionality factor in the rate equation that indicates the relationship between the rate of a chemical reaction and the concentrations of reactants.
03

Define 'A'

'A' stands for the pre-exponential factor, also known as the frequency factor. It basically provides a measure of the frequency of the collisions in the correct orientation.
04

Define 'Ea'

'Ea' stands for the activation energy measured in J/mol. It is the minimum energy required to initiate a chemical reaction.
05

Define 'R'

'R' is the universal gas constant. In this equation it is usually given the value of 8.314 J/(mol 鈥� K).
06

Define 'T'

'T' represents the absolute temperature measured in Kelvin.

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Most popular questions from this chapter

In the nuclear industry, workers use a rule of thumb that the radioactivity from any sample will be relatively harmless after 10 half-lives. Calculate the fraction of a radioactive sample that remains after this time. (Hint: Radioactive decays obey first-order kinetics.)

Consider this elementary step: $$ X+2 Y \longrightarrow X Y_{2} $$ (a) Write a rate law for this reaction. (b) If the initial rate of formation of \(\mathrm{XY}_{2}\) is \(3.8 \times 10^{-3} \mathrm{M} / \mathrm{s}\) and the initial concentrations of \(X\) and \(Y\) are \(0.26 M\) and \(0.88 M\), what is the rate constant of the reaction?

For each of these pairs of reaction conditions, indicate which has the faster rate of formation of hydrogen gas: (a) sodium or potassium with water, (b) magnesium or iron with \(1.0 \mathrm{M} \mathrm{HCl}\), (c) magnesium rod or magnesium powder with \(1.0 \mathrm{M} \mathrm{HCl}\), (d) magnesium with \(0.10 M \mathrm{HCl}\) or magnesium with \(1.0 \mathrm{M} \mathrm{HCl}\).

These data were collected for the reaction between hydrogen and nitric oxide at \(700^{\circ} \mathrm{C}\) : \(2 \mathrm{H}_{2}(g)+2 \mathrm{NO}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{N}_{2}(g)\) $$ \begin{array}{cllc} \text { Experiment } & {\left[\mathrm{H}_{2}\right]} & {[\mathrm{NO}]} & \text { Initial Rate }(\mathrm{M} / \mathrm{s}) \\ \hline 1 & 0.010 & 0.025 & 2.4 \times 10^{-6} \\ 2 & 0.0050 & 0.025 & 1.2 \times 10^{-6} \\ 3 & 0.010 & 0.0125 & 0.60 \times 10^{-6} \end{array} $$ (a) Determine the order of the reaction. (b) Calculate the rate constant. (c) Suggest a plausible mechanism that is consistent with the rate law. (Hint: Assume the oxygen atom is the intermediate.)

A quantity of \(6 \mathrm{~g}\) of granulated \(\mathrm{Zn}\) is added to a solution of \(2 M \mathrm{HCl}\) in a beaker at room temperature. Hydrogen gas is generated. For each of the following changes (at constant volume of the acid) state whether the rate of hydrogen gas evolution will be increased, decreased, or unchanged: (a) \(6 \mathrm{~g}\) of powdered \(\mathrm{Zn}\) is used; \((\mathrm{b}) 4 \mathrm{~g}\) of granulated \(\mathrm{Zn}\) is used; \((\mathrm{c})\) \(2 M\) acetic acid is used instead of \(2 M \mathrm{HCl} ;\) d) temperature is raised to \(40^{\circ} \mathrm{C}\).
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