AgNO3 is added gradually to a solution that is 0.050 M in Cl^- and 0.020 M in CrO4^2-. With K_sp(AgCl) = 1.8 x 10^-10 and K_sp(Ag2CrO4) = 2.0 x 10^-12, find the percentage of the original chloride still in solution when Ag2CrO4 just starts to precipitate, in units of 10^-2 percent (two decimals).

JEE Advanced levelNumerical answerDifficulty 3 of 3ie210

$AgNO X_{3}$ is added gradually to a solution that is $0.050 M$ in $Cl X^{-}$ and $0.020 M$ in $CrO X_{4} X^{2 -}$ . With $K_{s p} (AgCl) = 1.8 \times 1 0^{- 10}$ and $K_{s p} (Ag X_{2} CrO X_{4}) = 2.0 \times 1 0^{- 12}$ , find the percentage of the original chloride still in solution when $Ag X_{2} CrO X_{4}$ just starts to precipitate, in units of $1 0^{- 2}$ percent (two decimals).

Numerical answer type, answer in x 10^-2 percent, tolerance 0.03.

Ag X_{2} CrO X_{4}

starts at

[Ag X^{+}] = 2.0 \times 1 0^{- 12} /0.020 = 1.0 \times 1 0^{- 5} M

. Then

[Cl X^{-}] = 1.8 \times 1 0^{- 10} /1.0 \times 1 0^{- 5} = 1.8 \times 1 0^{- 5} M

. Fraction left

= 1.8 \times 1 0^{- 5} /0.050 \times 100 = 0.0360%

, which is 3.60 in units of

1 0^{- 2}

percent.