The following equilibrium exists in a closed vessel in `1L` capacity `A(g)+3B(g)hArr4C(g)`
initial cocentration of `A(g)` is equal to that `B(g)`. The equilibrium concentration of `A(g)` and `C(g)` are equal. `K_(c)` for the reaction is

Options

A. 0.08
B. 0.8
C. 8
D. 80

Answer

C

Explanation

`{:(,A(g),+,3B(g),hArr,4C(g)),("Eqm. conc",C(1-alpha),,C(1-3alpha),,4Calpha):}`
At eqm. `[A]_("eqm.")=[C]_("eqm.")`
`C(1-alpha)=4Calpha`
`5alpha=1`
`alpha=1//5`
`:. [A]_("eqm.")=C(1-alpha)=C(1-1//5)=4C//5`
`[B]_("eqm.")=C(1-alpha)=C(1-3//5)=2C//5`
`[C]_("eqm.")=4C alpha=4C//5`
`K_(C)=([C]^(4))/([A].[B]^(3))=((4C//5)^(4))/((4C//5)(2C//5)^(3))`
`=(4^(4))/(4xx2^(3))=(4^(3))/(2^(3))=2^(3)=8`