By Lee Johnson
Updated Aug 30, 2022
A solution is a homogeneous mixture of a solvent (usually water) and a solute that has been fully dissolved. The volume of the solution represents the combined amount of both components. To quantify a solution’s concentration you need two pieces of data: the quantity of solute and the total volume of the solution.
The most general definition of concentration is the ratio of solute to total solution, expressed in the same units. For example, adding 30 mL of hydrochloric acid to 270 mL of water yields a 30 mL / 300 mL × 100 = 10 % solution by volume:
\(\text{Concentration (in percent)} = \frac{\text{Amount of solute}}{\text{Total amount of solution}} \times 100\)
In chemistry we more often use molarity, the number of moles of solute per liter of solution. One mole corresponds to the substance’s molar mass in grams.
When you dilute a solution, the product of its initial molarity and volume remains constant:
\(M_i V_i = M_f V_f\)
Here, M is molarity and V is volume; the subscripts i and f denote initial and final values. If you know three of the four variables, you can solve for the fourth.
Example: You have 0.5 L of a 2 M solution and want a 0.5 M final concentration. Rearranging gives:
\(V_f = \frac{M_i V_i}{M_f}\)
Thus, \(V_f = \frac{2\text{ M} \times 0.5\text{ L}}{0.5\text{ M}} = 2\text{ L}\). You must dilute the mixture to 2 L.
Use the same equation with any consistent unit system (e.g., gallons) by expressing molarity in moles per that unit.
To find the final concentration when combining two solutions, compute the total moles of solute and the total volume, then divide:
\(\text{Final concentration} = \frac{\text{Total solute}}{\text{Total solution}}\)
Example: Mix a 2 % (by mass) salt solution weighing 100 g with a 10 % salt solution weighing 150 g.
The first contains 0.02 × 100 g = 2 g salt; the second contains 0.10 × 150 g = 15 g salt. Total salt = 17 g; total solution = 250 g. Final concentration = 17 g / 250 g = 0.068, or 6.8 %.
These straightforward calculations let you determine final concentrations without relying on specialized calculators.
