How milliliters of a 9.0 M H_2SO_ solution are needed to make 0.35 L of a 3.5 M solution?

1 Answer
Sep 29, 2016

You will need "140 mL" of "9.0 M H"_2"SO"_4" to make "350 mL" of a "3.5 M" solution.

Explanation:

The unit for molarity (M) is "moles of solute"/"liters of solution"="mol/L".

When diluting a solution, the amount of solute remains constant, but the volume of the solution increases.

The formula for the dilution of a solution is given below:

"M"_1"V"_1"=M"_2"V"_2",

where "M" is molarity and "V" is volume of the solution in liters (L).

Known
"M"_1="9.0 M"="9.0 mol/L"
"M"_2="3.5 M"="3.5 mol/L"
"V"_2="0.35 L"

Unknown
"V"_1"

Solution
Rearrange the dilution formula to isolate "V"_1". Substitute the known values into the equation and solve.

"V"_1=("M"_2"V"_2)/("M"_1)

"V"_1=(3.5cancel"M"xx"0.35 L")/(9.0cancel"M")="0.14 L" rounded to two significant figures

"V"_1=0.14 cancel"L"xx(1000 "mL")/(1 cancel"L")="140 mL" rounded to two significant figures