Engineering
Chemistry
Integrated Rate Law
Order of Reaction and Law of Mass Action
Ideal Gas Equation
Question
The gas phase decomposition of dimethyl ether follows first order kinetics:
CH3OCH3(g) → CH4(g) + H2(g) + CO(g)
The reaction is carried out in a constant volume container at 50°C and has a half life of 14.5 minutes. Initially, only dimethyl ether is present at a pressure of 0.40 atm. What is the total pressure of the system after 12 minutes? (Assume the ideal gas behaviour.)
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Solution
Pt = Po[ekt]
Pt = 0.225
CH3OCH3 → CH4 + H2 + CO
f = 0 amp; .40, amp;0 amp;0 amp;0
f = t amp; 40,amp;.40 − x, amp;x, amp;x,amp;x
0.40 − x = 0.225
x = 0.40 − 0.225 = 0.1746 atm
total pressure = 0.40 + 2x
= 0.40 + 0.349
= 0.749 atm