What volume of water should be added to 500 mL of a 1.0 mol/L CuSO_4 (aq) solution to dilute it to 0.5 mol/L?

Dec 1, 2016

In order to obtain a volume of $\text{1 L}$, $\text{500 mL}$ of water must be added to the original solution of $\text{500 L}$.

Explanation:

The symbol for molarity, M, pronounced molar, has the unit mol/L.

When diluting solutions, use the equation ${M}_{1} {V}_{1} \times {M}_{2} {V}_{2}$, where ${M}_{1}$ is the initial molarity in mol/L, ${M}_{2}$ is the final molarity, ${V}_{1}$ is the initial volume in Liters, and ${V}_{2}$ is the final volume in Liters.

Known
${M}_{1} = \text{1.0 mol/L CuSO"_4}$
${V}_{1} = 500 \cancel{\text{mL"xx(1"L")/(1000cancel"mL")="0.5 L}}$
${M}_{2} = \text{0.5 mol/L CuSO"_4}$

Unknown
${V}_{2}$

Solution
Rearrange the equation to isolate ${V}_{2}$. Substitute the known values into the equation and solve.

${V}_{2} = \frac{{M}_{1} {V}_{1}}{M} _ 2$

V_2=(1.0cancel"mol/L"xx0.5"L")/(0.5cancel"mol/L")="1 L"

In order to obtain a volume of $\text{1 L}$, $\text{500 mL}$ of water must be added to the original solution of $\text{500 mL}$.