Chapter 20, Problem 26E

The decomposition of dimethyl ether at $504°\text{C}$ is
   ${\left({\text{CH}}_{\text{3}}\right)}_{\text{2}}\text{O}\left(\text{g}\right)\to {\text{CH}}_{\text{4}}\left(\text{g}\right)+{\text{H}}_{\text{2}}\left(\text{g}\right)+\text{CO}\left(\text{g}\right)$

The following data are partial pressures of dimethyl ether (DME) as a function of time: $t=0s$, $P_{\text{OMG}}=312$ mmHg; 390s, 264 mmHg; 777s, 224 mmHg; 1195 s, 187 mmHg; 3155 s, 78.5 mmHg.

1. Show that the reaction is first order.
2. What is the value of the rate constant, k?
3. What is the total gas pressure at 390s?
4. What is the total gas pressure when the reaction has gone to completion?
5. What is the total gas pressure at t=1000s?