From the Arrhenius equation, predict how
a. increasing the experimental activation energy affects the rate constant for a reaction.

Verified step by step guidance

1. Understand the Arrhenius equation: The Arrhenius equation is given by \( k = A e^{-\frac{E_a}{RT}} \), 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. Identify the role of activation energy (\( E_a \)) in the equation: Activation energy is the minimum energy required for a reaction to occur. It is represented in the exponent of the exponential term in the Arrhenius equation.
3. Analyze the effect of increasing \( E_a \): As the activation energy \( E_a \) increases, the value of the exponent \( -\frac{E_a}{RT} \) becomes more negative.
4. Consider the exponential function's behavior: The exponential function \( e^x \) decreases as \( x \) becomes more negative. Therefore, increasing \( E_a \) leads to a decrease in the value of \( e^{-\frac{E_a}{RT}} \).
5. Conclude the effect on the rate constant \( k \): Since the exponential term decreases with an increase in \( E_a \), the overall rate constant \( k \) also decreases. This means that the reaction will proceed at a slower rate.

Key Concepts

Arrhenius Equation

The Arrhenius equation describes the temperature dependence of reaction rates, expressed as k = A * e^(-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 temperature in Kelvin. This equation illustrates how the rate constant changes with temperature and activation energy, providing insight into the kinetics of chemical reactions.

Activation Energy (Ea)

Activation energy is the minimum energy required for a chemical reaction to occur. It represents the energy barrier that reactants must overcome to form products. A higher activation energy means that fewer molecules have sufficient energy to react at a given temperature, leading to a slower reaction rate and a lower rate constant.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law of a reaction, indicating the speed at which a reaction proceeds. It is influenced by factors such as temperature and activation energy. According to the Arrhenius equation, as the activation energy increases, the rate constant decreases, resulting in a slower reaction rate.