What is the molality of a 21.6% (by mass) aqueous solution of phosphoric acid (#H_3PO_4#)?

Question

Wyatt Adkins · Accepted Answer

#"0.241 molal"#

As you know, molality is defined as moles of solute, which in your case is phosphoric acid, #"H"_3"PO"_4#, divided by kilograms of solvent, which is of course water.

#color(blue)(b = n_"solute"/m_"solvent")#

This means that in order to calculate the amount of solute and solvent in a random sample of solution, you must use the solution's percent concentration by mass.

Since you're dealing with percentages, you can make the calculations easier by picking a #"100.0-g"# sample of this solution. According to the given percent concentration, this solution will contain #"21.6 g"# of phosphoric acid.

Recall that the mass of the solution, which contains the solute and the solvent, is used to compute the percent concentration by mass.

Thus, the sample will additionally comprise

#m_"sample" = m_"solute" = m_"solvent"#

#m_"water" = "100.0 g" - "21.6 g" = "78.4 g"#

Remember that you must use the conversion factor to convert the solvent's mass from grams to kilograms.

#"1 kg" = 10^3"g"#

#78.4 color(red)(cancel(color(black)("g"))) * "1 kg"/(10^3color(red)(cancel(color(black)("g")))) = 78.4 * 10^(-3)"g"#

Now, use the compound's molar mass to determine how many moles of phosphoric acid are in this sample.

#21.6 color(red)(cancel(color(black)("g"))) * ("1 mole H"_3"PO"_4)/(97.995color(red)(cancel(color(black)("g")))) = "0.2204 moles H"_3"PO"_4#

Consequently, the molality of the solution will be

#b = "0.2204 moles"/(78.4 * 10^(-3)"kg") = color(green)("2.81 molal")#

Three sig figs are used to round the result.

SIDE NOTE The molality of the solution must be the same regardless of what sample you pick. I highly recommend redoing the calculations using a different starting sample #-># the molality will once again be #"0.241 molal"#.

Mateo Aguilar · Answer

undefined The molality of a 21.6% (by mass) aqueous solution of phosphoric acid (H3PO4) is approximately 9.94 mol/kg.