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Chapter 14: Problem 58

Indicate whether each statement is true or false. (a) If you measure the rate constant for a reaction al different temperatures, you can calculate the overall enthalpy change for the reaction. (b) Exothermic reactions are faster than endothermic reactions. (c) If you double the temperature for a reaction, you cut the activation energy in half.

Short Answer

Expert verified
(a) True - By using the Arrhenius and van 't Hoff equations, we can determine the overall enthalpy change (\(\Delta H\)) for the reaction. (b) False - The rate of a reaction is determined by its activation energy, not whether it is exothermic or endothermic. (c) False - Doubling the temperature affects the rate constant, not the activation energy, which is a characteristic property of the reaction.

Step by step solution

01

a) Enthalpy change calculation from rate constants at different temperatures

The statement is true. By measuring the rate constants for a reaction at different temperatures, we can use the Arrhenius equation to calculate the activation energy and then apply the van 't Hoff equation to determine the overall enthalpy change (\(\Delta H\)) for the reaction.
02

b) Exothermic vs. Endothermic reaction rates

The statement is false. The rate of a reaction is determined by its activation energy and not by whether the reaction is exothermic or endothermic. Lower activation energy usually results in faster reactions; however, both exothermic and endothermic reactions can have a range of activation energies.
03

c) Doubling the temperature and its effect on activation energy

The statement is false. Doubling the temperature of a reaction does not necessarily cut the activation energy in half. The relationship between temperature and the rate constant is given by the Arrhenius equation: \(k = Ae^{-\frac{Ea}{RT}}\), where \(k\) is the rate constant, \(A\) is the pre-exponential factor, \(Ea\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin. Doubling the temperature will affect the rate constant but not the activation energy itself, as it is a characteristic property of the reaction.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Enthalpy Change
Enthalpy change, symbolized by \(\Delta H\), is a measure of the total energy change in a chemical reaction. When we talk about enthalpy change, we focus on the heat absorbed or released, keeping pressure constant. It is critical in determining whether a process is energy-releasing or energy-absorbing.

When a reaction involves a change in temperature, the rate constants can be measured and analyzed against the Arrhenius and van 't Hoff equations. These help calculate both the activation energy and the overall enthalpy change. The Arrhenius equation is given by: \[ k = Ae^{-\frac{Ea}{RT}}\]Where:
  • \(k\) is the rate constant.
  • \(A\) is the pre-exponential factor, a constant for each chemical reaction.
  • \(Ea\) is the activation energy.
  • \(R\) is the gas constant.
  • \(T\) is the temperature in Kelvin.
The van 't Hoff equation further aids in identifying \(\Delta H\) from these rate constants, showing the enthalpy change associated with this reaction.
Exothermic Reactions
Exothermic reactions are those that release energy, typically in the form of heat, during the course of the reaction. This release of energy means that the enthalpy change, \(\Delta H\), is negative for exothermic reactions.

One common misconception is that exothermic reactions are inherently faster than endothermic reactions. However, the speed of a chemical reaction is primarily determined by the activation energy, not whether it's exothermic or endothermic. A lower activation energy indicates a potentially faster reaction as it requires less energy for the reactants to form products.

Exothermic reactions can have a wide range of activation energies, meaning some may occur rapidly, while others progress more slowly. Reaction conditions, such as temperature and the presence of catalysts, also play a significant role in the reaction rate.
Activation Energy
Activation energy, denoted as \(Ea\), is the minimum energy that reactant molecules must possess to transform into products. It serves as the energy barrier that needs to be overcome for a reaction to proceed.

The Arrhenius equation, \(k = Ae^{-\frac{Ea}{RT}}\), illustrates how the rate constant \(k\) is influenced by temperature \(T\) and activation energy \(Ea\). Contrary to a common misconception, changing the temperature of a reaction affects the rate constant \(k\), but not the activation energy \(Ea\) itself.

Doubling the temperature will increase the reaction rate, given that the system can achieve higher energy levels more frequently, therefore reducing the time needed for reactant molecules to surpass the activation energy threshold. However, this does not modify \(Ea\) directly; instead, it impacts how frequently the reactants can reach the required energy state to react.

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Most popular questions from this chapter

(a) The reaction \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+\) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)\) is first order with in \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(a q)\) and zero-order in \(\mathrm{H}_{2} \mathrm{O}\). At \(300 \mathrm{~K}\) the rate constant equals \(3.30 \times 10^{-2} \mathrm{~min}^{-1} .\) Calculate the half- life at this temperature. \((\mathbf{b})\) If the activation energy for this reaction is \(80.0 \mathrm{~kJ} / \mathrm{mol}\), at what temperature would the reaction rate be doubled?

Consider the hypothetical reaction \(2 \mathrm{~A}+\mathrm{B} \longrightarrow 2 \mathrm{C}+\mathrm{D}\). The following two-step mechanism is proposed for the reaction: $$ \begin{array}{l} \text { Step } 1: \mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}+\mathrm{X} \\\ \text { Step } 2: \mathrm{A}+\mathrm{X} \longrightarrow \mathrm{C}+\mathrm{D} \end{array} $$ \(\mathrm{X}\) is an unstable intermediate. (a) What is the predicted rate law expression if Step 1 is rate determining? (b) What is the predicted rate law expression if Step 2 is rate determining? (c) Your result for part (b) might be considered surprising for which of the following reasons: (i) The concentration of a product is in the rate law. (ii) There is a negative reaction order in the rate law. (iii) Both reasons (i) and (ii). (iv) Neither reasons (i) nor (ii).

Consider a hypothetical reaction between \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\) that is zero order in A, second order in B, and first order in C. (a) Write the rate law for the reaction. (b) How does the rate change when [A] is tripled and the other reactant concentrations are held constant? (c) How does the rate change when [B] is doubled and the other reactant concentrations are held constant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (e) By what factor does the rate change when the concentrations of all three reactants are doubled? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

The oxidation of \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3}\) is accelerated by \(\mathrm{NO}_{2}\). The reaction proceeds according to: $$ \begin{array}{l} \mathrm{NO}_{2}(g)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{SO}_{3}(g) \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) \end{array} $$ (a) Show that, with appropriate coefficients, the two reactions can be summed to give the overall oxidation of \(\mathrm{SO}_{2}\) by \(\mathrm{O}_{2}\) to give \(\mathrm{SO}_{3} .\) (b) Do we consider \(\mathrm{NO}_{2}\) a catalyst or an intermediate in this reaction? (c) Would you classify NO as a catalyst or as an intermediate? (d) Is this an example of homogeneous catalysis or heterogeneous catalysis?

Consider the following reaction: $$ 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ (a) The rate law for this reaction is first order in \(\mathrm{H}_{2}\) and second order in NO. Write the rate law. \((\mathbf{b})\) If the rate constant for this reaction at \(1000 \mathrm{~K}\) is \(6.0 \times 10^{4} \mathrm{M}^{-2} \mathrm{~s}^{-1}\), what is the reaction rate when \([\mathrm{NO}]=0.035 \mathrm{M}\) and \(\left[\mathrm{H}_{2}\right]=0.015 \mathrm{M} ?(\mathbf{c})\) What is the reaction rate at \(1000 \mathrm{~K}\) when the concentration of \(\mathrm{NO}\) is increased to \(0.10 \mathrm{M},\) while the concentration of \(\mathrm{H}_{2}\) is \(0.010 \mathrm{M} ?\) (d) What is the reaction rate at \(1000 \mathrm{~K}\) if \([\mathrm{NO}]\) is decreased to \(0.010 \mathrm{M}\) and \(\left[\mathrm{H}_{2}\right]\) is increased to \(0.030 \mathrm{M} ?\)
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