# An aqueous solution has a mass of 490 grams containing 8.5 xx 10^"-3" gram of calcium ions. What is the concentration of calcium ions in this solution?

Jun 7, 2017

$\text{17 ppm}$

#### Explanation:

Judging by the values you have, the most helpful concentration that can be calculated here is that in parts per million, ppm.

A solution's ppm concentration tells you the number of grams of solute present for every

${10}^{6} = 1 , 000 , 000$

grams of solution. Now, notice that you can approximate the mass of the solution, which is equal to

$\text{mass solution" = "490 g" + "0.0085 g}$

$\text{mass solution = 490.0085 g}$

to be equal to the mass of water, the solvent.

$\text{490.0085 g " ~~ " 490 g}$

You can thus say that, in your case, a $\text{1 ppm}$ solution will contain $\text{1 g}$ of calcium cations for every ${10}^{6}$ $\text{g}$ of water.

Use the known composition of the solution as a conversion factor to calculate the number of grams of calcium cations present in ${10}^{6}$ $\text{g}$ of solution.

10^6 color(red)(cancel(color(black)("g solution"))) * (8.5 * 10^(-3)color(white)(.)"g Ca"^(2+))/(490color(red)(cancel(color(black)("g solution")))) = "17.35 g Ca"^(2+)

Since this represents the number of grams of calcium cations present in ${10}^{6}$ $\text{g}$ of solution, you can say that the solution's ppm concentration is

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{concentration" = "17 ppm Ca}}^{2 +}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for your values.