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?

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.