Question

The mole fraction of sodium hydroxide in a saturated aqueous solution is 0.310. What is the molality of the solution? Answer is 24.9 but I do not know how to arrive to that answer

Answer 1

is this all the info given?

Answer 2

no volumes?

Answer 3

You don't need volumes for this question!

If the mole fraction of NaOH is 0.31 (i.e. 31% of moles of stuff in the solution are NaOH), then let's say there are 31 mol of NaOH. That means there are 69 mol of H2O.

Molarity is given by moles/volume. Multiplying by the molar mass, you can find that 69 mol of H2O = 1242 g of H2O. The density of H2O is 1 g/mL, meaning we have 1242 mL, or 1.242 L of H2O, which is the volume of solution (volume given by aqueous NaOH is negligible).

So for molarity: 31 mol / 1.242 L = 24.9 M

Answer 4

Thankyou @matt101. Your explanation is very helpful.

Answer 5

wait but it asks for molality which equals mol of solute(naoh)/kg solvent
not Molarity

Answer 6

can I arrive at the same answer using molality?

Answer 7

I see it is the same thing except to substitute the 1242 mL to g and then change that to Kg
so 31 mol/1.242 kg will equal the same answer as what you found

Answer 8

That's right! Sorry didn't read the question carefully. You wouldn't need to worry about density for this question and I could've just stopped after finding the mass of H2O.