# Why does adding sodium chloride to a saturated solution of lead chloride reduce the solubility of PbCl_2?

Mar 19, 2016

This is a standard problem in solubility equilibria; the solubility of $P b C {l}_{2}$ depends on the concentration of ions FROM ALL SOURCES.

#### Explanation:

We can write the solubility expression in this way:

$P b C {l}_{2} \left(s\right) r i g h t \le f t h a r p \infty n s P {b}^{2 +} + 2 C {l}^{-}$, is the reaction, AND

${K}_{s p} = \left[P {b}^{2 +}\right] {\left[C {l}^{-}\right]}^{2}$ is the solubility expression; $s p$ stands for solubility product, and ${K}_{s p}$ has been measured for a variety of salts at various temperatures.

The solubility expression depends on just the concentration of the lead and chloride ions; from where the ions come makes no difference. So if $\left[C {l}^{-}\right]$ is artificially raised (by adding sodium chloride), it logically follows that $\left[P {b}^{2 +}\right]$ must be correspondingly reduced in order for the solubility expression to be obeyed. The only way for $\left[P {b}^{2 +}\right]$ to be reduced is for more $P b C {l}_{2}$ to precipitate. The same effect would pertain if I added lead nitrate, a soluble lead salt. $\left[P {b}^{2 +}\right]$ would increase, and how would $\left[C {l}^{-}\right]$ evolve?

Such a phenomenon is known as $\text{salting out}$. It pushes the solubility equilibrium to the left hand side as WRITTEN. IF you were trying to isolate a precious metal, i.e. gold or platinum or rhodium, you want to salt out the precious metal salt and leave little of its ions in solution.

$\text{MORE ADVANCED TREATMENT,}$
$\text{2nd year analytical chemistry:}$

Given what I have said above, it might seem that I could reduce $\left[P {b}^{2 +}\right]$ to any desired level, simply by ramping up the concentration of chloride/halide ion. At very high concentrations of halide, however, soluble complex ions of lead may occur, i.e. ${\left[P b {X}_{4}\right]}^{2 -}$. For simple solubility equilibria, however, the formation of these complex ions may be ignored.