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

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Answer 1 · 2016-09-29T20:37:10

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

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