# Question #10c19

Aug 15, 2016

You also need the percent composition of the solution. Here's how to do the calculation with a specific example.

#### Explanation:

Example

What is the molarity of an 87.0 % (m/m) solution of phosphoric acid that has a molality of 68.3 mol/kg and a density of 1.46 g/mL?

Solution

Step 1: Assume some convenient amount of phosphoric acid solution.

I choose to assume a mass of 1 kg of the solution. Then

${\text{Mass of H"_3"PO"_4 = 1000 color(red)(cancel(color(black)("g solution"))) × ("87.0 g H"_3"PO"_4)/(100 color(red)(cancel(color(black)("g solution")))) = "870 g H"_3"PO}}_{4}$

Step 2: Calculate the mass of water

$\text{Mass of water" = "1000 g - 870 g" = "130 g}$

Step 3: Calculate the moles of ${\text{H"_3"PO}}_{4}$

${\text{Moles of H"_3"PO"_4 = 870 color(red)(cancel(color(black)("g H"_3"PO"_4))) × ("1 mol H"_3"PO"_4)/(98.00 color(red)(cancel(color(black)("g H"_3"PO"_4)))) = "8.878 mol H"_3"PO}}_{4}$

Step 4: Calculate the volume of the solution

$\text{Volume" = 1000 color(red)(cancel(color(black)("g solution"))) × "1 mL solution"/(1.46 color(red)(cancel(color(black)("mL solution")))) = "684.9 mL}$

Step 5: Calculate the molarity of the solution

$\text{Molarity" = "moles"/"litres" = "8.878 mol"/"0.6849 L" = "13.0 mol/L}$