How does rate constant of second order reaction depend on time?
The rate constant is independent of time and is a function of temperature.
This means that high temperature and low activation energy favor larger rate constants, and thus speed up the reaction. Because these terms occur in an exponent, their effects on the rate are quite substantial. (UC Davis)
For a second order reaction, the rate of decay of a chemical, C is given as:
`(dC)/dt = -kC^2`
where, k is the rate constant and C is the concentration of chemical. If we solve this equation, we end up with a simplified form:
`1/C_t = 1/C_0 + kt`
where, C0 is the initial concentration of the chemical.
The concentration of chemical at any time is a function of initial concentration and is also dependent on time elapsed.The rate constant k has units of per molar per second (inverse of concentration and inverse of time).
The rate constant is a function of temperature (and not time) and this relation is given by Arrhenius equation as:
`k = Ae^(-E_a/(RT))`
where, Ea is the activation energy, A is a constant and R is the Universal gas constant.