Question #497d6

1 Answer
Jun 18, 2015

The mole fraction of sucrose in your solution is 0.018.


Molality is defined as moles of solute, in your case sucrose, per kilograms of solvent, in your case water.

To make the calculations easier, you can assume that your 1 molal solution contains 1 mole of sucrose in 1 kg of water.

To get the mole fraction of sucrose, you need to determine how many total moles are present in your solution. Since you know that you have 1 mole of sucrose, all you need to determine is how many moles of water you get in 1 kg, or 1000 g, of water.

To do that, use water's moalr mass

#1000cancel("g") * "1 mole water"/(18.02cancel("g")) = "55.49 moles"# #H_2O#

Thus, the mole fraction of sucrose in your solution will be

#chi_"sucrose" = (1cancel("mole"))/((1 + 55.49)cancel("moles")) = 1/56.49 = "0.0177"#

I'll leave the answer rounded to two sig figs, despite the fact that you only have one sig fig for the molality of the solution

#chi_"sucrose" = color(green)("0.018")#