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)`

Answer

A

Explanation

The equilibrium constant is related to standard free energy 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 ^(@) = DeltaH ^(@) - T Delta S`
Given that `DeltaH^(@) = 308.3 - 400 xx 0. 857 =- 34.5 kJ =- 34500 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. 5046or K = 3.1959 xx 10 ^(4)`