Answer to Question #142937 in Physics for mickey

Question

The decomposition of SO2Cl2 (g) → SO2 (g) + Cl2 (g) is a first order, and the reaction has a half-life of
245 minutes at 600 K. If you begin with 3.6 x 10-3 mol of SO2Cl2 in a 1.0 L flask, how long will it take
for the amount of SO2Cl2 to decrease to 2.00 x 10-4 mol?

Answer 1

Find the decomposition constant:

$$\lambda=\frac{\text{ln}2}{t_{1/2}}.$$

Now, write the expression that describes how the amount of substance changes with time:

$$n(t)=n_0e^{-\lambda t}=n_0e^{-\frac{\text{ln}2}{t_{1/2}}t},\\\space\\ t=\frac{\text{ln}\frac{n_0}{n(t)}}{\frac{\text{ln}2}{t_{1/2}}},\\\space\\ t=\frac{\text{ln}\frac{3.6\cdot10^{-3}}{2\cdot10^{-4}}}{\frac{\text{ln}2}{245}}=1022\text{ min}.\text{}$$