Calculate the equilibrium constant for the the reaction given below at 400K, if `Delta H ^(@) = 77.2 kJ mol ^(-1) and Delta S ^(@) = 122JK ^(-1) mol ^(-1) , PCl _(s (s)) to PCl _(3 (g)) + Cl _(2 (g))`

Options

A. `1.958 xx 10 ^(-3)`
B. `1.958 xx 10 ^(-4)`
C. `1. 958 xx 10 ^(-2)`
D. `1. 958 xx 10 ^(2)`

Answer

B

Explanation

`Delta H ^(@) = 77.2 kJ mol ^(-1) , Delta S ^(@) = 122 JK ^(-1) mol ^(-1)`
`T = 400 K therefore Delta G ^(@) = DeltaH ^(@) - T DeltaS ^(@), DeltaG ^(@)= 77299 - 400 xx 122 = 28400 J`
Also we have `- DeltaG ^(@) = 2. 303 RT log _(10) K _(C) ` where `K _(C)` is equilbeium constant
`therefore - 28400 = 2.303 xx 8.314 xx 400 log _(10) K _(C) therefore K _(C) = 1. 958xx 10 ^(-4)`