Question #3acdc
1 Answer
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
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
#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
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
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.