SATHEE: Chemical Kinetics - Result Question 70

Chemical Kinetics - Result Question 70

####69. The gas phase decomposition of dimethyl ether follows first order kinetics

$C H_{3} - O - C H_{3} (g) ⟶ C H_{4} (g) + H_{2} (g) + C O (g)$

The reaction is carried out in a constant volume container at $500^{\circ} C$ and has a half-life of $14.5 m i n$ . Initially only dimethyl ether is present at a pressure of $0.40 a t m$ . What is the total pressure of the system after $12 m i n$ ? Assume ideal gas behaviour.

$(1993, 4 M)$

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Solution:

$C H_{3} - O - C H_{3} (g) ⟶ C H_{4} (g) + H_{2} (g) + C O (g)$

At 12 min : $0.40 - p$

Total pressure $= 0.4 + 2 p$

Also $k \times 12 = \ln \frac{0.40}{0.40 - p} = \frac{\ln 2}{14.5} \times 12 = 1.77 \Rightarrow p = 0.175$

$\Rightarrow$ Total pressure $= 0.4 + 2 p = 0.4 + 2 \times 0.175 = 0.75 a t m$

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Chemical Kinetics - Result Question 70

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