Question

mole fraction of sucrose in water is 0.1 the molality of sucrose in the aqueous solution is

Answer 1

Molality is moles solute in 1 kg of solvent ( in this case water ) 

The Molar mass of water = 18g/mol 

mol H2O in 1000g water = 55.55 mol

Let mol of solute = X mol 

Total mol in solution = 55.55 + X 

From definition: 

mol fraction solvent = X / ( 55.55+X ) 

0.1 = X / (55.55+X) 

X = 0.1 x (55.55+X) 

X = 5.555 + 0.1X 

X - 0.1X = 5.555 

0.9X = 5.555 

X = 5.555/0.9 

X = 6.17 mol sucrose in 1.0kg of water