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Ch.15 - Chemical Equilibrium
All textbooksBrown 15th EditionCh.15 - Chemical EquilibriumProblem 69c
Chapter 15, Problem 69c

(c) If the temperature is raised by 100 K, does the forward rate constant kf increase by a larger or smaller amount than the reverse rate constant kr?

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Identify the relationship between temperature and rate constants using the Arrhenius equation: \( k = A e^{-\frac{E_a}{RT}} \), where \( k \) is the rate constant, \( A \) is the pre-exponential factor, \( E_a \) is the activation energy, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.
Understand that the rate constant \( k \) increases with an increase in temperature because the exponential term \( e^{-\frac{E_a}{RT}} \) becomes larger as \( T \) increases.
Recognize that the magnitude of the increase in \( k \) depends on the activation energy \( E_a \). A higher \( E_a \) means a more significant change in \( k \) with temperature.
Compare the activation energies for the forward and reverse reactions. If \( E_{a,\text{forward}} > E_{a,\text{reverse}} \), the forward rate constant \( k_f \) will increase by a larger amount than the reverse rate constant \( k_r \) when temperature is raised.
Conclude that the change in rate constants with temperature is more pronounced for reactions with higher activation energies, and thus, the forward rate constant \( k_f \) will increase by a larger amount than the reverse rate constant \( k_r \) if its activation energy is higher.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Arrhenius Equation

The Arrhenius equation describes how the rate constant of a reaction depends on temperature. It states that the rate constant (k) increases exponentially with an increase in temperature, due to the increased kinetic energy of molecules, which enhances the frequency of effective collisions. The equation is given by k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
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Activation Energy

Activation energy (Ea) is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. Different reactions have different activation energies, which influence how sensitive the rate constants (k_f and k_r) are to changes in temperature. A lower activation energy typically results in a greater increase in the rate constant with temperature.
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Temperature Dependence of Reaction Rates

The temperature dependence of reaction rates indicates that as temperature increases, the rate of reaction generally increases due to higher molecular motion and collision frequency. However, the extent of this increase can vary between forward and reverse reactions, depending on their respective activation energies. Understanding this relationship is crucial for predicting how changes in temperature will affect k_f and k_r.
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Related Practice
Textbook Question

Ozone, O3, decomposes to molecular oxygen in the stratosphere according to the reaction 2 O3(𝑔) ⟢ 3 O2(𝑔). Would increasing the pressure by decreasing the size of the reaction vessel favor the formation of ozone or of oxygen?

Textbook Question

(a) Is the dissociation of fluorine molecules into atomic fluorine, F2(𝑔) β‡Œ 2 F(𝑔), an exothermic or endothermic process?

Textbook Question

(b) If the temperature is raised by 100 K, does the equilibrium constant for this reaction increase or decrease?

Textbook Question

When 2.00 mol of SO2Cl2 is placed in a 2.00-L flask at 303 K, 56% of the SO2Cl2 decomposes to SO2 and Cl2: SO2Cl2(g) β‡Œ SO2(g) + Cl2(g) (a) Calculate Kc for this reaction at this temperature.

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