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.
