Aqueous Solution Dilutions

Worked NaOH Chemistry Dilution Problem

Stock solutions serve as a source for making dilutions.
Stock solutions serve as a source for making dilutions. Nicholas Rigg, Getty Images

Most laboratories keep stock solutions of common or frequently used solutions of high concentration. These stock solutions are used for dilutions. A dilution is prepared by adding more solvent, usually water, to obtain a dilute or less-concentrated solution. The reason dilutions are made from stock solutions is that it's easier to measure quantities accurately for the concentrated solutions. Then, when the solution is diluted, you have confidence in its concentration.

Here's an example of how to determine how much of a stock solution is needed in order to prepare a dilution. The example is for sodium hydroxide, a common lab chemical, but the same principle could be used to calculate other dilutions.

How To Solve a Dilution Problem

Calculate the amount of 1 M NaOH aqueous solution needed to make 100 mL of 0.5 M NaOH aqueous solution.

Formula needed:
M = m/V
where M = molarity of solution in mol/liter
m = number of moles of solute
V = volume of solvent in liters

Step 1:
Calculate the number of moles of NaOH needed for 0.5 M NaOH aqueous solution.
M = m/V
0.5 mol/L = m/(0.100 L)
solve for m:
m = 0.5 mol/L x 0.100 L = 0.05 mol NaOH.

Step 2:
Calculate the volume of 1 M NaOH aqueous solution that gives that gives the number of moles of NaOH from step 1.
M = m/V
V=m/M
V = (0.05 moles NaOH)/(1 mol/L)
V = 0.05 L or 50 mL

Answer:
50 mL of 1 M NaOH aqueous solution is needed to make 100 mL of 0.5 M NaOH aqueous solution.

To prepare the dilution, pre-rinse the container with water. Add the 50 mL of sodium hydroxide solution. Dilute it with water to reach the 100 mL mark. Note: do not add 100 ml of water to 50 ml of solution. This is a common mistake. The calculation is for a certain total volume of solution.

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Helmenstine, Todd. "Aqueous Solution Dilutions." ThoughtCo, Jun. 22, 2016, thoughtco.com/aqueous-solution-dilutions-example-609551. Helmenstine, Todd. (2016, June 22). Aqueous Solution Dilutions. Retrieved from https://www.thoughtco.com/aqueous-solution-dilutions-example-609551 Helmenstine, Todd. "Aqueous Solution Dilutions." ThoughtCo. https://www.thoughtco.com/aqueous-solution-dilutions-example-609551 (accessed November 24, 2017).