The solubility product of a salt having general formula $\mathrm{MX}_{2}$, in water is: $4 \times 10^{-12}$. The concentration of $\mathrm{M}^{2+}$ ions in the aqueous solution of the salt is

JEE Main · 2005 · 08 May 2005 · Offline · Equilibrium

The solubility product of a salt having general formula

MX_{2}

, in water is:

4 \times 1 0^{- 12}

. The concentration of

M^{2 +}

ions in the aqueous solution of the salt is

Answer: (B)

For a salt of the type

MX X_{2}

dissolving as

MX X_{2} M X^{2 +} + 2 X X^{-}

, let the solubility be

s

; then

[M X^{2 +}] = s

and

[X X^{-}] = 2 s

. The solubility product is

K_{s p} = s (2 s)^{2} = 4 s^{3}

. Setting

4 s^{3} = 4 \times 1 0^{- 12}

gives

s^{3} = 1 0^{- 12}

and

s = 1 0^{- 4}

mol L

^{- 1}

, and since

[M X^{2 +}]

equals

s

, the metal-ion concentration is

1.0 \times 1 0^{- 4}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option