Equal volumes of BaCl2 and Na2SO4 solutions are mixed (K_sp of BaSO4 = 1.1x10^-10). In which of the following pairs of initial concentrations will BaSO4 precipitate?

Ba^2+ 6x10^-5 M and SO4^2- 2x10^-5 M

Ba^2+ 4x10^-5 M and SO4^2- 2x10^-5 M

Ba^2+ 6x10^-5 M and SO4^2- 2x10^-5 M

Ba^2+ 1x10^-5 M and SO4^2- 1x10^-5 M

Ba^2+ 2x10^-4 M and SO4^2- 1x10^-6 M

Ba^2+ 4x10^-5 M and SO4^2- 2x10^-5 M

JEE Main levelOne or more correct optionsDifficulty 2 of 3ia187

Equal volumes of $BaCl X_{2}$ and $Na X_{2} SO X_{4}$ solutions are mixed ( $K_{s p}$ of $BaSO X_{4} = 1.1 \times 1 0^{- 10}$ ). In which of the following pairs of initial concentrations will $BaSO X_{4}$ precipitate?

A $Ba X^{2 +}$ $6 \times 1 0^{- 5} M$ and $SO X_{4} X^{2 -}$ $2 \times 1 0^{- 5} M$
B $Ba X^{2 +}$ $1 \times 1 0^{- 5} M$ and $SO X_{4} X^{2 -}$ $1 \times 1 0^{- 5} M$
C $Ba X^{2 +}$ $2 \times 1 0^{- 4} M$ and $SO X_{4} X^{2 -}$ $1 \times 1 0^{- 6} M$
D $Ba X^{2 +}$ $4 \times 1 0^{- 5} M$ and $SO X_{4} X^{2 -}$ $2 \times 1 0^{- 5} M$

Mixing equal volumes halves each concentration, so

Q = (c_{1} /2) (c_{2} /2)

. The values of

Q

are

2.5 \times 1 0^{- 11}

2.0 \times 1 0^{- 10}

5.0 \times 1 0^{- 11}

2.4 \times 1 0^{- 10}

respectively. Precipitation occurs only when

Q > 1.1 \times 1 0^{- 10}

, i.e. in the second and fourth pairs.