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

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.

Key Concepts

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.

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.

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.