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# Aqueous Solution Dilutions

## Worked Chemistry Problems

Stock solutions serve as a source for making dilutions.

Nicholas Rigg, Getty Images
Concept
Most laboratories keep stock solutions of common or frequently used solutions of high concentration. These stock solutions are used for dilutions.

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

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