Aqueous Solution 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.