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Chapter 13: Problem 86

According to the Arrhenius equation, does the activation energy of a chemical reaction depend on temperature? Explain your answer.

Short Answer

Expert verified
Answer: No, the activation energy (Ea) of a chemical reaction does not depend on temperature according to the Arrhenius equation. Ea is a constant for a specific reaction, while the rate of the reaction depends on temperature through the exponential term in the equation.

Step by step solution

01

Arrhenius Equation

The Arrhenius equation describes the relationship between the rate constant (k) of a chemical reaction and temperature (T). It is expressed as follows: k = Ae^(-Ea/RT) where k is the rate constant, A is the pre-exponential factor (which depends on the reaction but not on temperature), Ea is the activation energy, R is the gas constant (8.314 J/mol K), and T is the temperature in Kelvin.
02

Analyzing the Activation Energy

In the equation, the activation energy (Ea) is a constant for a particular reaction, independent of the temperature. It represents the minimum energy required for the reactants to undergo a chemical reaction.
03

Temperature Dependency

The temperature dependency in the Arrhenius equation is represented by the exponential term, e^(-Ea/RT). As the temperature (T) increases, the exponent becomes less negative, and the exponential term becomes larger. This means that the rate constant (k) of the reaction increases with temperature, and the reaction occurs faster.
04

Conclusion

According to the Arrhenius equation, the activation energy (Ea) of a chemical reaction does not depend on temperature. The activation energy is a constant for a specific reaction, while the rate of the reaction depends on temperature through the exponential term in the equation.

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Most popular questions from this chapter

The rate laws for the thermal and photochemical decomposition of \(\mathrm{NO}_{2}\) are different. Which of the following mechanisms are possible for the thermal decomposition of \(\mathrm{NO}_{2},\) and which are possible for the photochemical decomposition of \(\mathrm{NO}_{2}\) ? For the thermal decomposition, Rate \(=k\left[\mathrm{NO}_{2}\right]^{2},\) and for the photochemical decomposition, Rate \(=k\left[\mathrm{NO}_{2}\right]\). a. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \stackrel{\text { fast }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{O}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{3}(g)+\mathrm{O}(g) \stackrel{\text { fast }}{\mathrm{N}_{2} \mathrm{O}_{2}(g)} \stackrel{\mathrm{fast}}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{2}(g)+\mathrm{O}_{2}(g)\) \(\quad \quad \mathrm{NO}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\mathrm{fast}}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. \(\quad \mathrm{NO}_{2}(g) \stackrel{\text { slow }}{\longrightarrow} \mathrm{N}(g)+\mathrm{O}_{2}(g)\) \(\begin{aligned} \mathrm{N}(g)+& \mathrm{NO}_{2}(g) \frac{\mathrm{fast}}{\mathrm{N}_{2} \mathrm{O}_{2}(g)} \mathrm{N}_{2} \mathrm{O}_{2}(g) \\ & \stackrel{\text { fast }}{\longrightarrow} \mathrm{NO}(g) \end{aligned}\)

What effect does doubling the initial concentration of a reactant have on the half-life in a reaction that is second order in the reactant?

In the presence of water, NO and \(\mathrm{NO}_{2}\) react to form nitrous acid (HNO,) by the following reaction: $$\mathrm{NO}(g)+\mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{HNO}_{2}(a q)$$ When the concentration of NO or \(\mathrm{NO}_{2}\) is doubled, the initial rate of reaction doubles. If the rate of the reaction does not depend on \(\left[\mathrm{H}_{2} \mathrm{O}\right],\) what is the rate law for this reaction?

Nitric oxide (NO) can be removed from gas-fired power-plant emissions by reaction with methane as follows: \(\mathrm{CH}_{4}(g)+4 \mathrm{NO}(g) \rightarrow 2 \mathrm{N}_{2}(g)+\mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) Write an equation relating each of the following pairs of rates: a. The rate of formation of \(\mathrm{N}_{2}\) to the rate of formation of \(\mathrm{CO}_{2}\) b. The rate of formation of \(\mathrm{CO}_{2}\) to the rate of consumption of NO c. The rate of consumption of \(\mathrm{CH}_{4}\) to the rate of formation of \(\mathrm{H}_{2} \mathrm{O}\)

Under what circumstances is the activation energy of a reaction proceeding in the forward direction less than the activation energy of it happening in reverse?
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