Question

The rate law for the decomposition of PH3 is, R = -d[PH3]/dt = k[PH3]. It takes 120 s for the concentration of 0.84 M PH3 to decrease to 0.21 M. How much time is required for 1.5 M PH3 to decrease to 0.56 M?

Answer 1

We are given the rate as R = -d[PH₃]/dt = k[PH₃] where [PH₃] represents concentration of PH₃. We can take [PH₃] on the left-hand side and then find the integrated rate law.

The integrated rate law can be written as ln[PH₃]_t - ln[PH₃]₀ = -kt

Here [PH₃]_t and [PH₃]₀ represent the concentrations of PH₃ at time t seconds and at time 0 seconds respectively.

From the integrated rate law, ln[PH₃]_t = ln[PH₃]₀ - kt

ln(0.21) = ln(0.84) - k(120)

k = 0.01155 sec^-1

Substituting the value of rate constant k in the integrated rate law in order to find the required time,

ln(0.56) = ln(1.5) - (0.01155)t

t = 85.306 seconds