Answer to Question #143587 in Physics for Johannes Steven

Question

1. The decomposition of SO₂Cl₂ = SO₂ + Cl₂ is a first order, and the reaction has a half life of 245 minutes at 600K. 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

The decomposition constant is

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

The amount of substance left after time t :

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