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Q.

The correct relationship between molarity (M) and molality (m) is (d = density of the solution, in Kg L-1, M2 = molar mass of the solute in kg mol-1)

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a

large M, = ,frac{{md}}{{1 + m{M_2}}}

 

b

M, = ,frac{m}{{1 + m{M_2}d}}

 

c

M, = ,frac{{1 + m{M_2}}}{{md}}

 

d

M, = ,frac{{1 + md}}{{m{M_2}}}

 

answer is A.

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Detailed Solution

Given  M=Molarity of solution    ;     m=molality of solution

        M2=MW of solute in kg     ;      d= density of solution in kg/lit

molality = frac{no.of;moles;of;solute(n)}{1;kg;of;solvent}

molality = nsolute (in magnitude)

Wsolvent = 1 kg

Wsolute(in kg) = nsolute X MW of solute in kg

we know ,  nsolute = m ;   MW of solute in kg = M2

therefore ;W_{solute};=mM_2

W_{solution};=W_{solvent}+W_{solute};;(in;kg)=1+mM_2

d_{solution}=frac{W_{sol}in;kg}{V_{sol}inlit}

V_{sol}=frac{W_{sol}}{d_{sol}}=frac{1+mM_2}{d}

Molarity (M)= n_{solute}Xfrac{1}{V_{solution}}

                                  =m;X;frac{1}{frac{1+mM_2}{d}}

therefore;M=frac{md}{1+mM_2}    

 

 

 

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