# Aqueous Solution Dilutions

## Worked NaOH Chemistry Dilution Problem

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