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?

1 Answer
Dec 1, 2016

Answer:

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"#.