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(a) In the following equilibrium N(2)O(4...

(a) In the following equilibrium `N_(2)O_(4)(g)hArr2NO_(2)(g)` when 5 moles of each are taken, the temperature is kept at `298K` the total pressure was found to be 20 bar. Given that `DeltaG_(f)^(@)(N_(2)O_(4))=100kJ, DeltaG_(f)^(@)(NO_(2))=50kJ`
(i) Find `DeltaG` of the reaction.
(ii) The direction of th reaction in which the equilibrium shifts.
(b) A graph is plotted for a real gas which follows van der Waals' equation with `pV_(m)` taken on `Y`-axis and `p` on `X`-axis.
Find the intercept of the ine where `V_(m)` is molar volume.

Text Solution

Verified by Experts

`N_(2)O_(4) rarr 2NO_(2)`
`DeltaG^(@) = 2DeltaG_(f)^(@)(NO_(2))- DeltaG_(f)^(@)(N_(2)O_(4)) = 0`
Also `DeltaG^(@) = -RT ln K = 0, K = 1`
Let the reaction shifts in forward direction.
`N_(2)O_(4) rarr 2NO_(2)`
`implies K = (5+2x)^(2)/(10+x)^(2) xx 10-x/5-x xx 20 = 1 implies 81x^(2)+405x+450 = 0 implies x = -1.66 and -3.33`
Both values of x indicates that reaction actually proceeds in backward direction.
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