Temperature Dependence And Arrhenius Equation

Temperature Dependence of Reaction Rates

Most chemical reactions speed up when you turn up the heat. As a general rule of thumb, for a chemical reaction, the rate constant is nearly doubled for every $10^{\circ}\text{C}$ (or $10\,\text{K}$) rise in temperature.

But how do we calculate this precisely?

Example 3.9: Calculating Activation Energy

Problem. The rate constants of a reaction at $500\,\text{K}$ and $700\,\text{K}$ are $0.02\,\text{s}^{-1}$ and $0.07\,\text{s}^{-1}$ respectively. Calculate the values of $E_a$ and $A$.

Givens:

• $T_1 = 500\,\text{K}$
• $k_1 = 0.02\,\text{s}^{-1}$
• $T_2 = 700\,\text{K}$
• $k_2 = 0.07\,\text{s}^{-1}$

Example 3.10: Finding Rate Constant at a New Temperature

Problem. The first order rate constant for the decomposition of ethyl iodide at $600\,\text{K}$ is $1.60 \times 10^{-5}\,\text{s}^{-1}$. Its energy of activation is $209\,\text{kJ/mol}$. Calculate the rate constant of the reaction at $700\,\text{K}$.

Givens:

• $T_1 = 600\,\text{K}$, $k_1 = 1.60 \times 10^{-5}\,\text{s}^{-1}$
• $T_2 = 700\,\text{K}$, $k_2 = ?$
• $E_a = 209\,\text{kJ/mol} = 209000\,\text{J/mol}$

Effect of a Catalyst

A catalyst is a substance that increases the rate of a reaction without undergoing any permanent chemical change itself.

How does it do this? According to intermediate complex theory, a catalyst participates in a reaction by forming temporary bonds with the reactants. This creates an intermediate complex that exists briefly before decomposing to yield the products and regenerate the catalyst.