**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

**Answer:**

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