Question

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

Answer 1

Let molar mass of protein $A = x g / mol$

Let molar mass of protein $B = y g / mol$

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

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

$\pi_{ A }=\pi_{ B }$

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

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