Question

What is the fluoride ion concentration for a saturated solution of BaF 2 if the K sp for BaF 2 is 1.8 × 10 -7 ?

Answer 1

$\\ \rm\rightarrowtail BaF_2\longrightarrow Ba^{2+}+2F-$

• BaF_2 be x
• Ba2+ is also x
• F- is 2x

Now

$\\ \rm\Rrightarrow K_{sp}=[Ba^2+][F-]^2$

$\\ \rm\Rrightarrow 1.8\times 10^{-7}=x(2x)^2$

$\\ \rm\Rrightarrow 4x^3=1.8\times 10^{-7}$

$\\ \rm\Rrightarrow x^3=0.45\times 10^{-7}$

$\\ \rm\Rrightarrow x=\sqrt[3]{0.000000045}$

$\\ \rm\Rrightarrow x=0.00376M$

$\\ \rm\Rrightarrow x=3.8\times 10^{-3}M$

So

$\\ \rm\Rrightarrow [F-]=2x=7.6\times 10^{-3}M$