# Question #b0189

Sep 16, 2017

The mass-balance equation is $2 \left[\text{Sr"^"2+"] = 3["PO"_4^"3-}\right]$.

#### Explanation:

In a solubility product calculation, a mass-balance equation relates the equilibrium concentrations of the different species in the solution to each another.

For example, assume that you were asked to calculate the molar solubility $s$ of strontium phosphate.

You would probably start by writing something like this:

$\textcolor{w h i t e}{m m m m m m} \text{Sr"_3("PO"_4)_2"(s)" ⇌ "3Sr"^"2+""(aq)" + "2PO"_4^"3-""(aq)}$
$\text{E/mol·L"^"-1} : \textcolor{w h i t e}{m m m m m m m m m m l l} 3 s \textcolor{w h i t e}{m m m m m l} 2 s$

You are saying that

$\left[\text{Sr"^"2+}\right] = 3 s$ and $\left[\text{PO"_4^"3-}\right] = 2 s$

Then,

$\textcolor{b l u e}{2 \left[\text{Sr"^"2+"] = 3["PO"_4^"3-}\right]}$

This is the mass-balance equation.

In effect, to get the mass-balance equation, you multiply each concentration by the charge on the ion.