Answer
$Solubility = 1.817 \times 10^{-3} g/L$
Work Step by Step
$Kps (LaF_3) = 2 \times 10^{-19}$
1. Write the Kps equation:
$Kps (LaF_3) = [La^{3+}] * [F^-]^3$
$[La^{3+}] = x$
$[F^-] = 3x$
2. Now, find the solubility:
$2 \times 10^{-19} = [x] * [3x]^3$
$2 \times 10^{-19} = x * 27x^3$
$2 \times 10^{-19} = 27x^4$
$7.407 \times 10^{-21} = x^4$
$x = 9.277 \times 10^{-6}M$
3. Covert that number to g/L.
$mm(LaF_3) = 138.9 + 19*3 = 195.9g/mol$
$mass = n(moles) * mm$
$mass = 9.277 \times 10^{-6} * 195.9$
$mass = 1.817 \times 10^{-3}g$
$Solubility = 1.817 \times 10^{-3} g/L$
