Calculate the equilibrium constant for a reaction at 400 K given that `DeltaH^(@) = 308.3kJ mol^(-1) and Delta S = 0. 857 kJ K ^(-1) mol ^(-1) at 400 K.`

Options

A. `3.1959 xx 10 ^(4)`
B. `6.35 xx 10 ^(4)`
C. `9. 25 xx 10 ^(4)`
D. `8.35 xx 10 ^(4)`

Explanation

The equilibrium constant is related to standard free enenrgy change by the reaction `Delta G ^(@) =- RT ln K = - 2. 303 RT log K ` and free energy can be obtained from the relation
`Delta G ^(@) = Delta H ^(@) - T Delta S`
Given that `Delta H ^(@) = 308 . 3 kJ mol ^(-1) : Delta S = 0. 857 kJ K ^(-1) , T = 400 K.` Substituting values, we get
`Delta G ^(@) = 308.3 - 400 xx 0. 857 =- 34. 5 kJ =- 24 500 J`
Substituting value of `Delta G ^(@)` in the above equation , we get ` - 34500 =- 2. 303 xx 8. 314 xx 400 xx log K`
`log K = ( 34500)/( 7658.8) = 4. 5046 or K = 3.1959xx 10 ^(4)`