Question

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?

Answer 1

In order to obtain a volume of `"1 L"`, `"500 mL"` of water must be added to the original solution of `"500 L"`.

Explanation:

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

When diluting solutions, use the equation `M_1V_1xxM_2V_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="1.0 mol/L CuSO"_4"`
`V_1=500 cancel"mL"xx(1"L")/(1000cancel"mL")="0.5 L"`
`M_2="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=(M_1V_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 `"1 L"`, `"500 mL"` of water must be added to the original solution of `"500 mL"`.