In a system `A(s) hArr 2B(g) +3C (g)`
if the conc. Of C at equilibrium is increased by a factor of 2, it will cause the equilibrium concentration of B to change to

Options

A. two times the original value
B. one half of its original value
C. `2sqrt2` time the original value
D. `1//2sqrt2` time the original value

Answer

D

Explanation

`A(s) hArr 2B(g) +3C(g)`
Let, x and y be the concentrations of B and C at equilibrium respectively.
`therefore K_c =X^2Y^3` …………..(1)
Now, the concentration of C is changed from y to y. such that `y.=2y`. If x. is the new concentration of B
`therefore K_c=(X.)^2(y.)^3=(x.)^2(2y)^3` ........... (2)
From Eqs. (1) and (2)
`(x.)^2(8y^3)=x^2y^3`
`therefore x.=sqrt((x^2)/8)=x/(2sqrt2)`
`therefore` Equilibrium concentration of B changes to `1/(2sqrt2)` times the original value .