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 m2 = mass of solute M = molecular mass of solute
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