How to Calculate the Final Concentration of a Solution With Different Concentrations

By Michael Judge
Mixing solutions is often a part of a chemical process.

Scientists use units of concentration to describe the amount of a chemical substance dissolved in a given volume of liquid. There are many different units for this purpose, including percent by weight or volume, molarity and parts per million (ppm). When two solutions of the same chemical but having different concentrations are combined, the concentration of the resulting mixture will be different from either of the two starting solutions. You can calculate the concentration of the final mixture using a mathematical formula involving the volumes of the two combined solutions, as well as the initial concentrations of the two solutions.

Multiply, for each of the two solutions, the initial concentration of the solution by the volume of the solution which is measured out to make the combined mixture. For example, if you combined 80 milliliters (mL) of 300 ppm sodium chloride (NaCl) in water with 20 mL of 500 ppm NaCl, you would calculate 300 times 80 (equal to 24,000) and 500 x 20 (equal to 10,000).

Add together the products of the two previous calculations. Call this "x" to simplify subsequent calculations. For the example, you would add 24,000 and 10,000 to obtain x = 34,000.

Add together the two volumes of the starting solutions to find the total combined volume of the mixture. In the case of the example, you would add 80 mL and 20 mL to obtain 100 mL.

Divide the result of this most recent calculation into the value of "x." The result is the concentration of the solution made by combining the two initial solutions of differing concentrations, in the same units as your initial concentrations. For the example, you would calculate 34,000 divided by 100 to obtain a combined concentration of 340 ppm NaCl.


You can use any units you wish for the concentration values and volumes, so long as you use the same units for each of the two solutions.

About the Author

Michael Judge has been writing for over a decade and has been published in "The Globe and Mail" (Canada's national newspaper) and the U.K. magazine "New Scientist." He holds a Master of Science from the University of Waterloo. Michael has worked for an aerospace firm where he was in charge of rocket propellant formulation and is now a college instructor.