Question

The density of 3 molal sodium thiosulphate solution is 1.25g/ cm3.the mole fraction of sodium thiosulphate is ?

Answer 1

Hello Dear..

Here is the answer---


Given⇒

Density of Sodium Thiosulphate solution  = 1.25 g/cm³
Mass of 1000 cm³ of 3 M solution = 1.25 × 1000
= 1250 g.

No. of moles of Sodium Sulphate = 3 moles.
Molar mass of sodium thiosulphate = 158 g/mol.

∴ Mass of the Sodium Thiosulphate in 100 cm³ of solution = Molar mass of Sodium Thiosulphate × Number of Moles of Solute(Sodium Thiosulphate)
= 158 × 3
= 474 g.

∵ Mass of the Solution = Mass of the Solute + Mass of the Solvent 
∴ Mass of the Water = Mass of the Solution - Mass of Sodium Thiosulphate.
 = (1250 - 474) g.
= 776 g.

Now,
Moles of Solvent(Water) = Mass/Molar Mass
  = 776/18
[Since, Molar Mass of the Water = 18 grams]
 = 43.11 moles.


Now, Total Moles in the solution = Moles of Water + Moles of Sodium Thiosulphate.
= 3 + 43.11
= 46.11 moles.

Now, Using the Formula,

Mole Fraction of Sodium Thiosulphate = (Moles of Sodium Thiosulphate ÷ Total number of moles in a solution.
= 3/46.11
= 0.065 

∴ Moles Fraction of Sodium thiosulphate is 0.065.

↔↔↔

Hope it helps.

Have a Marvelous Day.

Answer 2

3 molal solution of sodium thiosulphate means that there are 3 moles of it per 1000g of solvent (H₂O). Hence, the number of moles of water would be 1000/18 = 55.55.
Mole fraction of sodium thiosulphate is the number of moles of it over total number of moles in the solution, which would be 3/(3+55.55) = 3/58.5 = 0.0513.