The gas phase decomposition of dimethyl ether follows first-order kinetics: CH3-O-CH3 → CH4(g) + H2(g) + CO(g). The reaction is carried out in a constant volume container at 500°C and has a half-life

Question

The gas phase decomposition of dimethyl ether follows first-order kinetics: CH3-O-CH3 → CH4(g) + H2(g) + CO(g). The reaction is carried out in a constant volume container at 500°C and has a half-life of 14.5 minutes. Initially, only dimethyl ether is present at a pressure of 4.0 atmosphere. What is the total pressure of the system (in atm) after 43.5 min? Assume ideal gas behaviour.

Prashant Kotian · Accepted Answer

Correct answer: 0011. 43.5 min is exactly 3 half-lives (3 × 14.5). The remaining pressure of ether is 4.0 / 2^3 = 0.5 atm. The pressure of ether that reacted is 3.5 atm. The decomposition yields 3 moles of gas per mole of ether, so the pressure of products is 3 × 3.5 = 10.5 atm. Total pressure = 0.5 + 10.5 = 11.0 atm. Therefore, correct answer is 0011.

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