The rate constant of a chemical reaction increases with temperature. This is because temperature provides the necessary activation energy required for reactant molecules to reach the transition state and convert into products. As the temperature increases, the average kinetic energy of the reactant molecules increases, leading to a higher probability of successful collisions and more frequent attainment of the activation energy. Consequently, the reaction rate increases, and the rate constant, which is a measure of the reaction rate, also increases.

The relationship between the rate constant (k) and temperature (T) is often described by the Arrhenius equation:

k = Ae^(-Ea/RT)

Where:

- A is the pre-exponential factor or frequency factor, which represents the frequency of collisions between reactant molecules with the correct orientation and sufficient energy.

- Ea is the activation energy of the reaction, which is the minimum energy required for the reactants to reach the transition state.

- R is the gas constant (8.314 J/mol*K)

-T is the absolute temperature in Kelvin

According to the Arrhenius equation, as temperature (T) increases, the exponential term e^(-Ea/RT) decreases, leading to an overall increase in the rate constant (k). Therefore, higher temperatures generally result in faster reaction rates due to more frequent successful collisions and a higher proportion of reactant molecules possessing the necessary activation energy.