Physical Chemistry

Give derivation of relation between molarity and mole fraction of solute

Ambasana

12 Years agoGrade

1 Answer

sumit kumar

12 Years ago

Let,

Number of moles solute =n₁
Number ofmoles solvent =n₂
Mass of solute =m₁
Mass of solvent =m₂
Molecular weight of solute =Mw₁
Molecular weight of solvent =Mw₂
Density solution =ρ
Volume of solution =V

molarity =M =
Mole fraction of solute =χ₁

so,
Molarity = n₁ / V …....(i)
χ₁ = n₁ / (n₁ + n₂) …...(ii)

Rearranging (i) and substituting into (ii)
χ₁ = MV / (MV + n₂) …..(iii)

But

ρ = (m₁ + m₂) / V …..(iv)

Also
m₁ = n₁ x Mw₁...(v)
(&

m₂ = n₂ x Mw₂…..(vi)

substituting (v) and (vi) into (4)
ρ = (n₁ x Mw₁ + n₂ x Mw₂) / V
or
ρ = (n₁ x Mw₁)/V + (n₂ x Mw₂) / V

Since n₁/V = M
ρ = M x mw₁ + (n₂/V) x Mw₂
or
n₂ = V x (ρ - M x Mw₁) / Mw₂

Substituting into (iii)
χ= MV / (MV + V x (ρ - M x Mw₁) / Mw₂)
or
χ= M / (M + (ρ - M x Mw₁) / Mw₂)

Thanks & Regards

Sumit Kumar

askIITinas Faculty