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    M = molarity of the solution
   m = molality of the solution
   d = density of the solution (in g. ml^-1)
   M¹ = gram molecular weight of solute
   Which of the following relations is correct

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\large m\, = \,\frac{M}{{1000d - M{M^1}}}

m\, = \,\frac{{M \times 1000}}{{\left( {1000 \times d} \right) - M{M^1}}}

m\, = \,\frac{{M \times 1000}}{{d + M{M^1}}}

answer is C.

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Detailed Solution

Molarity = \frac{n_{solute}}{1\;lit\;of\;solution}

magnitude of Molarity (M) = n_solute

V_solution=1 lit (1000ml) ; d_solution=d (in g/ml)

W_solution= (1000 X d) gm

W_solvent= W_solution- W_solute (in gms)

= 1000d - (n_soluteX GMW of solute)

But n_solute = Molarity ; GMW of solute = M¹

W_solvent = (1000 X d)- MM¹

molality = n_{solute} X\;\frac{1000}{W_{solvent}(gm) }

\therefore \;m=\frac{MX1000}{(1000Xd)-MM^1}

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M = molarity of the solution m = molality of the solution d = density of the solution (in g. ml-1) M1 = gram molecular weight of solute Which of the following relations is correct