The standard Gibbs energy change at 300 K for the reaction `2A hArr B+C` is 2494.2 J. At a given time, the composition of the reaction mixture is `[A]=(1)/(2), [B] =2` and `[C]=(1)/(2)`. The reaction proceeds in the : [R = 8.314 J/K/mol, e = 2.718]

Options

A. forward direction because `Q gt K_(c )`
B. reverse direction because `Q gt K_(c )`
C. forward direction because `Q lt K_(c )`
D. reverse direction because `Q lt K_(c )`

Answer

B

Explanation

`2A hArr B+C, Delta G^(@)=2494.2 J`
`Delta G^(@)=-2.303 RT log K_(c )`
`therefore - 2.303 RT log K_(c ) = 2494.2`
`-2.303xx8.314xx300 log K_(c ) = 2494.2`
`log K_(c )=-(2494.2)/(2.303xx8.314xx300)=0.4342`
`K_(c )=` antilog `(0.4342)=0.367`
Now `[A]=(1)/(2), [B]=2` and `[C]=(1)/(2)`
`Q_(c )=([C][B])/([A]^(2))=((1)/(2)xx2)/(((1)/(2))^(2))=4`
Since `Q_(c )gt K_(c )`, reaction will shift in backward direction.