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A gaseous compound X decomposes into gaseous products Y and Z according to first-order kinetics (X -> Y + Z). Initially only X is present. Ten minutes after the reaction begins, the partial pressure of X is 200 mmHg and the total pressure of the mixture is 300 mmHg. What is the rate constant for this reaction?

1. (1/600) ln 1.25 s⁻¹
2. (2.303/10) log 1.5 min⁻¹
3. (1/10) ln 1.25 s⁻¹
4. (2.303/600) log 1.5 s⁻¹

Correct answer: (1/600) ln 1.25 s⁻¹

Solution

Setting up P0 - x = 200 and P0 + x = 300 gives P0 = 250 mmHg and x = 50 mmHg. The rate constant k = (1/10 min)*ln(250/200) = (1/10)*ln(1.25) min⁻¹ = (1/600)*ln(1.25) s⁻¹.

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