1.

At `60^(@)C`, dinitrogen tetroxide is 50 per cent dissociated. Calculate the standard free energy change at this temperature and at one atmosphere.

Answer» `N_(2)O_(4)(g)hArr2NO_(2)(g)`
If `N_(2)O_(4 )`is 50% dissociated, the mole fraction of both the substances is given by
`X_(N_(2O_(4)))=(1.05)/(1+0.5):x_(No_(2))=(2xx0.5)/(1+0.5)`
`P_(N_(2O_(4)))=(0.5)/(1.5)xx1atm,P_(NO_(2))=(1)/(1.5)xx1atm`The equilibrium constant `K_(p)` is given by
`K_(p)=((P_No_(2))^(2))/(P_(N_(2O_(4))))=(1.5)/((1.5)^(2)(0.5))`
`=1.33 atm`.
Since
`Delta_(r)G^(Ө)=-RTlnK_(p)`
`Delta_(r)G^(Ө)=(-8.314JK^(-1)"mol"^(-1))xx(333K) xx(2.303)xx(0.1239)`
`=-763.8 "mol"^(-1)`


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