Mixing and Dilution
Consider an initial solution with molar concentration, C
i
, and volume, V
i
.
Note that the number
of mols of solute is thereby: C
i
× V
i
= n
i
.
To this solution, let us imagine adding a volume, V
2
, of a second (of the same type) characterized
by a concentration, C
2
. Again, note the number of moles added to the original solution is
n
2
= C
2
× V
2
.
The resulting, “final”, solution, will have a concentration, C
f
and volume, V
f
.
The basic rule is that
the final concentration of any solution formed by mixing two (or more)
solutions is: “the total amount of solute divided by the total amount of solvent/solution.”
The solvent/solution distinction depends on the particular concentration unit.
For molarity, the
denominator would be the total volume of solution.
Thus, we may write:
2
2
2
2
2
V
V
V
C
V
C
V
V
n
n
C
i
i
i
i
i
f
+
+
=
+
+
=
This expression is explicit for mixing two solutions.
More generally for the case of mixing “N”
different solutions:
+
+
+
+
+
+
=
=
∑
∑
=
=
3
2
1
3
3
2
2
1
1
1
1
V
V
V
V
C
V
C
V
C
V
V
C
C
N
i
i
N
i
i
i
f
For those of you with some statistics, the above equation is simply the weighted average formula.
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 Fall '07
 Warren
 Chemistry

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