How would I go about solving this problem? Can someone show me an equation that can be used?

Question

The decomposition of dimethyl ether at 504°C is a first-order reaction with a half-life of 27 min.

(CH3)2O(g) CH4(g) + H2(g) + CO(g)

(a) What will be the partial pressure of (CH3)2O(g) after 2.28 h if its initial partial pressure was 679 mm Hg?

(b) What will be the total gas pressure after 2.18 h? [Hint: (CH3)2O and its decomposition products are the only gases present in the reaction vessel.]

Can someone show me how to solve these problems (the equation I have to use)

Answer 1

For a you can use the first order decay constant. First, determine k from
k = 0.693/t_1/2
Then substitute Po, k, and t into
ln(Po/P) = kt. Note: You must convert the t_1/2 into hours (to use 2.28 hours in the problem) or leave the 27 min as is and convert the 2.28 hours into minutes.

After you know the partial pressure of the reactant and how much as decomposed, determine partial pressures of the products, then take the sum of all the gases.