1. Tardigrade
  2. Question
  3. Chemistry
  4. The gas phase decomposition of dimethyl ether follows first order kinetics CH3-O-CH3(g)arrow 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 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.

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Q. The gas phase decomposition of dimethyl ether follows first order kinetics
$CH_3-O-CH_3(g)\rightarrow CH_4(g)+H_2(g)+CO(g)$
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.

IIT JEEIIT JEE 1993Chemical Kinetics

Solution:

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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 $=0.4+2 p= 0.4+2 \times 0.175$
$=0.75\, atm$