In the system `A_((s))hArr2B_((g))+3C_((g))`, if the concentration of `C` at equilibrium is increased by a factor of `2`, it will cause the equilibrium concentration of `B` to change to:

Options

A. 2 times
B. `root2(2)` times the original value
C. 1/2 of the original value
D. `1/(root2(2))` times the original value

Answer

D

Explanation

`A(s) hArr 2B(g) + 3C(g)`
Let x and y be the concentration of B and C at equilibrium.
`K_c=x^2y^3` …(i)
Now, if concentration of C is changed to y. such that y.=2y
If x. is the new conc. Of B, then
`K_c=(x.)^2 (y.)^3 =(x.)^2 (2y)^3` ...(ii)
From (i) and (ii)
`(x)^2 8y^3 =x^2y^3`
`(x.)^2=x^2/8`
or `x.=sqrt(x^2/8)=x/root(2)(2)`
i.e., `1/root (2)(2)` times the original value.