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Q.

    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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a

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

 

b

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

 

c

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

 

d

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}

 

\therefore

magnitude of Molarity (M) = nsolute

Vsolution=1 lit (1000ml)  ;    dsolution=d (in g/ml)

Wsolution= (1000 X d) gm

Wsolvent= Wsolution - Wsolute  (in gms)

                = 1000d - (nsolute X GMW of solute)

But  nsolute = Molarity       ;       GMW of solute = M1

Wsolvent = (1000 X d)- MM1

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

 

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