Rate Constant in First Order Reaction

To determine the rate constant (k) for a first order reaction, you can use the integrated rate law for first order reactions. The integrated rate law is:

ln[A] = -kt + ln[A]₀

where [A] is the concentration of the reactant at time t, [A]₀ is the initial concentration of the reactant, and ln is the natural logarithm.

By plotting ln[A] versus t, you will get a straight line with a slope of -k. From the slope, you can determine the rate constant k.

Alternatively, if you know the half-life (t_1/2) of the reaction, you can use the relation:

k = 0.693 / t_1/2