For a particular first-order reaction, it takes 3.0 minutes for the concentration of the reactant to decrease to 25% of its initial value. what is the value for rate constant (in s-1) for the reaction?

We will use this formula for first order:

㏑[A] = - Kt + Ao

when we have t (given) = 30 min = 30 x 60 = 1800 s (we here convert time from min to second.

then we assume that the initial concentration Ao = 1

and the concentration of A (final concentration = 0.25

So by substitution:

㏑ (0.25) = - K * 1800 + ㏑ (1)

1.39 = K * 1800

∴ K = 0.00077 s^-1 or 7.7 x 10^-4