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Give derivation of relation between molarity and mole fraction of solute

Give derivation of relation between molarity and mole fraction of solute

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1 Answers

sumit kumar
askIITians Faculty 13 Points
9 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

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