1 mole of gas X is present in a closed adiabatic vessel fitted with a movable frictionless piston. The initial temperature of gas X is 300 K. The vessel in maintained at constant pressure of 1 atm. Ke

Question

1 mole of gas X is present in a closed adiabatic vessel fitted with a movable frictionless piston. The initial temperature of gas X is 300 K. The vessel in maintained at constant pressure of 1 atm. Keeping the pressure constant at 1 atm the reaction $(3 X (g) \to 2 Y (g); Δ_{r} H = - 30 kJ / mol)$ is started with the help of negligible amount of electric energy. If finally 75 mole % of X undergone reaction at constant pressure of 1 atm, find the final temperature (in K ) of reaction vessel.

Given: $C_{p, m} (X) = 40 J/K \cdot mol$ ; $C_{p, m} (Y) = 30 J/K \cdot mol$

Ignore the change in $Δ_{r} H$ value with the change in temperature.

TestHub · Accepted Answer

Mole of X reacted = 0.75 mole

Heat liberated at constant pressure $= 0.75 \times 10 kJ = 7.5 kJ$

mole of X remaining $= \frac{1}{4}$ mole

mole of Y formed $= \frac{3}{4} \times \frac{2}{3} = \frac{1}{2}$

$(\frac{1}{4} C_{p, m (X)} + \frac{1}{2} C_{p, m (Y)}) (Δ T) = q = 7500$

$Δ T = \frac{7500}{\frac{40}{4} + \frac{30}{2}} = 300$

Final temperature $= 300 + 300 \Rightarrow 600 K$

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