Chemistry Help?

Question

You take 20.0 g of a sucrose (C12H22O11) and NaCl mixture and dissolve it in  of water. The freezing point of this soluton is found to be -0.426°C. Assuming ideal behavior, calculate the mass percent compositon of the original mixture, and the mole fracton of sucrose in the original mixture. 

I know that answer is 72.8% sucrose and 27.2% sodium chloride; 
mole fraction of the sucrose is 0.313 but I do not know how to get it.

Answer 1

Step 1:

Total mass of the mixture is 20 g.

Freezing point of the solution is .

Let mass of the sucrose be grams.

Molar Mass of the sucrose is 324.496 g/mol

Amount of sucrose in moles is

Mass of Sodium chloride is grams.

Molar Mass of the Sodium chloride is 58.44 g/mol

Total mass of mixture =Mass of sucrose + Mass of the Sodium chloride.

.

Step 2:

Freezing point of water , where

is the change in temperature and ,

is the van 't Hoff factor,

is the molality of the solution and

is the molality depression constant = .

Freezing point : .

Here for sucrose is 1.

for sodium chloride is 2.

Substitute

Mass of the sucrose is 14.55 g.

Mass of the sodium chloride is 20-14.55 = 5.45 g.

Comments

Contd...

Step 3:

Mass percentage of the substance is .

Mass percentage of Sucrose:

Mass percentage of Sodium chloride:

Mole fraction of substance is

Mole fraction of sucrose:

Solution:

Mass percentage of Sucrose is 72.8%

Mass percentage of Sodium chloride is 27.25%

Mole fraction of sucrose is 0.3246.