Question

If $250c{m}^3$ of an aqueous solution containing $0.73g$ of a protein $A$ is isotonic with one litre of another aqueous solution containing $1.65g$ of a protein $B$, at $298K$, the ratio of the molecular mases of $A$ and $B$ is _____$\times 10^{-2}$ (to the nearest integer)

Answer 1

Answer: 177

Let molar mass of protein $A=xg/mol$

Let molar mass of protein $B=yg/mol$

${\pi }_A=$ osmotic pressure of protein $A=\frac{\left(\frac{0.73}{x}\right)}{0.25}RT$

${\pi }_B=$ osmotic pressure of protcin $B=\frac{\left(\frac{1.65}{y}\right)}{1}RT$

${\pi }_A={\pi }_B$

$\Rightarrow \left(\frac{0.73}{x\times 0.25}\right)RT=\left(\frac{1.65}{y}\right)RT$

$\Rightarrow \left(\frac{x}{y}\right)=\frac{0.73}{0.25\times 1.65}=1.769\cong 1.77$