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he first-order rate constant for the gas-phase decomposition of dimethyl ether, (CH3)2O → CH4 + H2 + CO is 3.2 ✕ 10−4 s−1 at 450°C. The reaction is carried out in a constant-volume container. Initially, only dimethyl ether is present, and the pressure is 0.336 atm. What is the pressure of the system after 7.7 min? Assume ideal-gas behavior. g

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Answer:

0.290 atm is the pressure of the system after 7.7min

Explanation:

The general first-order rate constant is:

ln [A] = -kt + ln [A]₀

Where [A] is concentration of A in time t,

K is rate constant, 3.2x10⁻⁴s⁻¹

[A]₀ is initial concentration = 0.336atm.

7.7 min are:

7.7min * (60s / 1min) = 462s

Solving:

ln [A] = -kt + ln [A]₀

ln [A] = -3.2x10⁻⁴s⁻¹*462s + ln [0.336atm]

ln [A] = -1.238

[A] =

0.290 atm is the pressure of the system after 7.7min

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