Chemical Kinetics - Result Question 70
####69. The gas phase decomposition of dimethyl ether follows first order kinetics
$$ CH _3-O-CH _3(g) \longrightarrow CH _4(g)+H _2(g)+CO(g) $$
The reaction is carried out in a constant volume container at $500^{\circ} C$ and has a half-life of $14.5 min$. Initially only dimethyl ether is present at a pressure of $0.40 atm$. What is the total pressure of the system after $12 min$ ? Assume ideal gas behaviour.
$(1993,4 M)$
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Solution:
- $CH _3-O-CH _3(g) \longrightarrow CH _4(g)+H _2(g)+CO(g)$
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 $=0.4+2 p=0.4+2 \times 0.175=0.75 atm$
