Question

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?

Answer 1

`"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

`"mass solution" = "490 g" + "0.0085 g"`

`"mass solution = 490.0085 g"`

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

`"490.0085 g " ~~ " 490 g"`

You can thus say that, in your case, a `"1 ppm"` solution will contain `"1 g"` of calcium cations for every `10^6` `"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` `"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` `"g"` of solution, you can say that the solution's ppm concentration is

`color(darkgreen)(ul(color(black)("concentration" = "17 ppm Ca"^(2+))))`

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