If I combine two solutions of known concentrations and volumes, can I calculate the concentration of the new solution by adding the two concentrations together and dividing the result by 2?

1 Answer
Apr 3, 2018

No.

Explanation:

Let's use an example. Say, we have a #"100 mL"# solution of #"0.4 M"# #HCl# and another #"150 mL"# solution of #"4 M"# #HCl#.
If we wanted to find the final concentration of #HCl#, we would need to use the formula for molarity:

#"molarity" = "number of moles"/"volume of solution (L)"#

For us, this would be:

#"molarity" = ("0.04 moles + 0.6 moles") / ("0.100 L + 0.150 L") = "2.56 M"#

Adding the concentrations together and then dividing the resulting value by #2# gives #(0.4 + 4) -: 2 = 4.4 -: 2 = "2.2 M"#. This is incorrect, because the answer should have been #"2.56 M"#.

On a more conceptual level, this method doesn’t work because it doesn’t take the volumes into account.
The initial volumes of the two solutions and the final volume of the mixed solution both affect the final concentration, but this method doesn’t take that into account.