If I believe it to be true, you don't need the density value unless you're wanting to convert from molarity to mole fraction; we can calculate mole fraction from molality directly without any other information.
We're given that we have a
All we have to do now is calculate the number of moles of water present, using its molar mass:
The mole fraction of
Here's what I got.
Assuming that the information you provided is correct and you're dealing with a
In your case, a
Now, to make the calculations easier, let's pick a sample fo this solution that contains exactly
Use the molar mass of water to convert the mass of the solvent to moles
#10^3 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "55.51 moles H"_2"O"#
Now, the mole fraction of sodium hydroxide,
In your case, you will have
#chi_ "NaOH" = (10.5 color(red)(cancel(color(black)("moles"))))/((10.5 + 55.51)color(red)(cancel(color(black)("moles")))) = color(darkgreen)(ul(color(black)(0.159)))#
The answer is rounded to three sig figs.
I highly recommend redoing the calculations using a different sample of solution, i.e. a solution that does not contain exactly
SIDE NOTE: If you're dealing with a
- pick a
#"1 L" = 10^3# #"mL"#sample of this solution
- use its density to find the total mass of the solution
- use the molar mass of sodium hydroxide to find the mass of the solute present in the sample
- calculate the mass of water present in the sample
- use the molar mass of water to find the number of moles of water
- calculate the mole fraction of sodium hydroxide as shown above