What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?
The rate constant of a reaction increases with increase in temperature. It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled. This happens because increasing the temperature increases the fraction of molecules that collide with energies greater than the activation energy (Ea).
This temperature dependence of rate constant can be represented quantitatively by the Arrhenius equation: k = A , where k is the rate constant, A is the Arrhenius factor (pre-exponential factor), Ea is the activation energy, R is the gas constant, and T is the temperature. The equation shows that increasing temperature leads to an exponential increase in the rate constant.
Explanation
The answer addresses both parts of the question as required. The first part explains the qualitative effect of temperature on rate constant (increase, nearly doubles for 10° rise). The second part provides the quantitative representation through the Arrhenius equation. Both points are directly derived from the textbook context provided.