$$1$$ 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 is maintained at constant pressure of $$1$$ atm. Keeping the pressure constant at $$1$$ atm the reaction (3X(g)→$$2Y(g)$$;Δ$$H=-30$$ $$kJ/mol)$$ is started with 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 : Cp,$$m(X)=40$$ $$J/K$$ mole, Cp,$$m(Y)=30$$ $$J/K$$ mole.

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 is maintained at constant pressure of $$1$$ atm. Keeping the pressure constant at $$1$$ atm the reaction (3X(g)→$$2Y(g)$$;Δ$$H=-30$$ $$kJ/mol)$$ is started with 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 : Cp,$$m(X)=40$$ $$J/K$$ mole, Cp,$$m(Y)=30$$ $$J/K$$ mole.

Infinity Learn · Accepted Answer

Mole of X reacted $$=$$ $$0.75$$ moleHeated liberated at constant pressure $$=$$ $$0.75$$ × $$10$$ kJ $$=$$ $$7.5$$ kJMole of X remaining $$=$$ $$14molemole$$ of Y formed $$=$$ $$34$$×$$23=1214Cp$$,$$m(X)+12Cp$$,$$m(Y)($$Δ$$T)=q=7500$$Δ$$T=7500404+302=300Final$$ temperature $$=$$ $$300$$ $$+$$ $$300$$ $$=$$ $$600$$ K

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