Question

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

Answer 1

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