Hi,

I'm having trouble with the following homework problem:

The first-order rate constant for the gas phase decomposition of dimethyl ether is 3.2 x 10–4 s–1 at 450 °C. The reaction is carried out in a constant volume container. Initially only the reactant, dimethyl ether, is present and the pressure is 0.325 atm. What is the pressure (in atm) of the reactant after 499 seconds? Assume ideal-gas behaviour.

CH_{3}OCH_{3} --> CH_{4} + H_{2} + CO_{2}

I'm confused about how to relate pressure with the equation I have in my notes for temperature dependent rate constants k = Ae^(-Ea/RT). Am I supposed to use the ideal gas law somehow?

Attempt:

Pressure at t=0 is 0.325 atm for CH_{3}OCH_{3}, 0 atm for products

Pressure at t = 499s is 0.325-x for dimethyl ether and x atm for products

Total pressure at 499s is P_{total} = 0.325 + 2x

But now I'm stuck because I don't know what to do with this expression for pressure.

Thanks.