Question

What is the molality of a 15.0 M solution of phosphoric acid with a density of 1.65 g/mL?

Answer 1

The molal concentration is 83.3 mol/kg.

Explanation:

Assume that you have one litre of the phosphoric acid solution.

Step 1. Calculate the mass of the solution

`"Mass of solution" = 1000 color(red)(cancel(color(black)("mL solution"))) × "1.65 g solution"/(1 color(red)(cancel(color(black)("mL solution")))) = "1650 g solution"`

Step 2. Calculate the mass of `"H"_3"PO"_4`

`"Mass of H"_3"PO"_4 = 15.0 color(red)(cancel(color(black)("mol H"_3"PO"_4))) × ("98.00 g H"_3"PO"_4)/(1 color(red)(cancel(color(black)("mol H"_3"PO"_4)))) = "1470 g H"_3"PO"_4`

Step 3. Calculate the mass of water

`"Mass of water = 1650 g - 1470 g = 180 g"`

So, the solution contains `"15.0 mol H"_3"PO"_4` and 180 g water.

Step 4. Calculate the moles of `"H"_3"PO"_4` in 1 kg water

`"Moles of H"_3"PO"_4 = 1000 color(red)(cancel(color(black)("g water"))) × ("15.0 mol H"_3"PO"_4)/(180 color(red)(cancel(color(black)("g water")))) = "83.3 mol H"_3"PO"_4`

∴ The molal concentration is 83.3 mol/kg.