Question

The first order reaction, SO2Cl2 --> SO2 + Cl2, has a half life of 8.75 hours at 593 K.?

How long will it take for the concentration of SO2CL2 to fall to 12.5% of its initial value?

Answer 1

Ans :-

Let initial concentration = [A]₀ = 100 M

Therefore, Concentration after time " t " = [A]_t = 100 - 12.5 % of 100 = 12.5 M

Half-life period for first order reaction is :

t_1/2 = 0.693 / k ...............(1)

k = rate constant = ?

t_1/2 = Half-life period = 8.75 hrs (Given)

So, from equation (1), we have

k = 0.693 / t_1/2 = 0.693 / 8.75 hrs = 0.0792 hrs^-1

Integrated rate equation for first order reaction is :

t = 2.303 / k log [A]₀ / [A]_t ...............(2)

t = 2.303 / 0.0792 hrs^-1 log 100 M / 12.5 M

t = 29.078 hrs log (8)

t = 29.078 hrs (0.9031)

t = 26.25 hrs