A) \[{{M}_{2}}=\left[ \frac{{{m}_{2}}}{\pi } \right]VRT\]
B) \[{{M}_{2}}=\left[ \frac{{{m}_{2}}}{V} \right]\frac{RT}{\pi }\]
C) \[{{M}_{2}}=\left[ \frac{{{m}_{2}}}{V} \right]\pi RT\]
D) \[{{M}_{2}}\left[ \frac{{{m}_{2}}}{V} \right]\frac{\pi }{RT}\]
Correct Answer: B
Solution :
For dilute solution, \[PV=nRT\] or \[\pi V=nRT\] or \[\pi =\frac{n}{V}RT\] \[\Rightarrow \] \[\pi V=\frac{{{m}_{2}}}{M}RT\] \[\Rightarrow \] \[M=\frac{{{m}_{2}}RT}{\pi V}\] where, \[\pi =\]osmotic pressure \[V=\]volume of solution \[n=\]number of moles of solute \[{{m}_{2}}=\]mass of solute \[M=\]molecular mass of solute
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