Question #3acdc

1 Answer
Feb 27, 2017

Here's how you can do that.

Explanation:

The idea here is that you need to work with a sample of this solution and figure out how many moles of propanol it contains.

As you know, molality is defined as the number of moles of solute present for every "1 kg" of solvent. In your case, propanol is the solute and water is the solvent.

To make the calculations easier, let's pick a sample of solution that contains exactly

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

of water. You know that water has a molar mass of "18.015 g mol"^(-1), which means that this solution will contain

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 propanol in this solution is defined as the ratio between the number of moles of propanol, let's say n_p, and the total number of moles present in solution.

In your case, this mole fraction is equal to

(n_p color(red)(cancel(color(black)("moles"))))/((n_p + 55.51)color(red)(cancel(color(black)("moles")))) = 0.1538

This means that you have

n_p = (n_p + 55.51) * 0.1538

(1 - 0.1538) * n_p = 55.51 * 0.1538

0.8462 * n_p = 8.5374 implies n_p = 8.5374/0.8462 = 10.09

Therefore, you know that a solution of propanol that contains "1 kg" of water and in which the solute has a 0.1538 mole fraction contains 10.09 moles of propanol.

You can thus say that the molality of the solution is equal to

color(darkgreen)(ul(color(black)("molality = 10.09 mol kg"^(-1))))

The answer is rounded to four sig figs, the number of sig figs you have for the mole fraction of propanol.