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.

Question

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. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/717c4a836140988d900b6eabb1ced1d6-.png" /> Total pressure =0.4+2 p Also k × 12= ln (0.40/0.40-p)=( ln 2/14.5) × 12=1.77 ⇒ p=0.175 ⇒ Total pressure =0.4+2 p= 0.4+2 × 0.175 =0.75 atm

Total pressure =0.4+2p Also k×12=ln0.40−p0.40​=14.5ln2​×12=1.77 ⇒p=0.175 ⇒ Total pressure =0.4+2p=0.4+2×0.175 =0.75atm

Total pressure $= 0.4 + 2 p$
Also $k \times 12 = ln \frac{0.40}{0.40 - p} = \frac{l n 2}{14.5} \times 12 = 1.77$
$\Rightarrow p = 0.175$
$\Rightarrow$ Total pressure $= 0.4 + 2 p = 0.4 + 2 \times 0.175$
$= 0.75 a t m$