An increase in temperature generally leads to an increase in the rate constant for a first-order reaction. This relationship is described by the Arrhenius equation, which relates the rate constant (k) to the temperature (T):
k = A * e^(-Ea/RT)
In this equation, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
According to the Arrhenius equation, as the temperature (T) increases, the exponential term e^(-Ea/RT) becomes larger, resulting in a higher rate constant (k). This means that the reaction proceeds more quickly at higher temperatures.
The reason behind this effect is that an increase in temperature provides more energy to the reactant molecules, enabling them to overcome the activation energy barrier more easily. As a result, a larger fraction of the molecules have sufficient energy to react, leading to a faster reaction rate.
It's important to note that the relationship between temperature and the rate constant is not linear but exponential, as shown in the Arrhenius equation. This highlights the significant impact temperature has on the rate of reaction for a first-order process.