An aqueous solution of X is 3 molal. find mole fraction of X

Question

Please solve this question and give details of solutions. 

Answer 1

n1 = moles of solute

 

n2 = moles of water (the solvent in this aqueous solution)

 

M2  = mass of water (kg)

 

W2 = molecular weight of water = 18 g/mol (approximately)

 

m = molality = (moles of solute) / (kg of solvent) = n1 / M2 = 3 mols/kg = 0.003 mols/g

 

x = mole fraction of solute = n1 / (n1 + n2)

 

Multiply numerator and denominator of mole fraction by 1/M2:

 

x  = n1 / (n1 + n2) = (n1/M2) / [(n1/M2) + n2/M2)]

 

n2 = M2/W2 ⇒ n2/M2 = 1/W2 ⇒

 

x = (n1/M2) / [(n1/M2) + 1/W2)]

 

We need to be consistent with the units, so I worked this in grams:

 

x = (0.003 mols/g) / [(0.003 mols/g) + 1/(18 g/mol)] = 0.003 / (0.003 + 1/18) = 0.0512