The decomposition of azo methane, at a certain temperature according to the equation $(\text{CH}_3)_2\text{N}_2 \rightarrow \text{C}_2\text{H}_6 + \text{N}_2$, is a first-order reaction. After $40\,\text{minutes}$ from the start, the total pressure developed is found to be $350\,\text{mm Hg}$ in place of the initial pressure of $200\,\text{mm Hg}$ of azo methane. The value of the rate constant $k$ is: