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?

1 Answer
Stefan V.
Jun 7, 2017

#"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.

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