Question

Insulin is dissolved in a suitable solvent and the osmotic pressure $\pi$ in atm of solutions of various concentrations C in $g/c{m}^3$ is measured at ${27}^o$C. The slope of plot of $\pi$ against C is found to be $4.1\times {10}^{-3}$ atm $c{m}^3$ $g^{-1}$. The molecular mass of insulin is?

• A. $6\times {10}^3$
• B. $3\times {10}^6$
• C. $6\times {10}^5$
• D. $3\times {10}^3$

Answer 1

The correct option is A $6\times {10}^3$

Osmotic pressure is given by,

$\pi =icRT$

where, $i$= Van't Hoff factor, preferably $1$ for perfect nonelectrolytes.

$c$= concentration

$R$= $0.082057L$ $atm/molK$

$T$= Temperature in $K$

If we plot $\pi$ vs $c$, the slope is $iRT$

$\therefore$ slope= $4\times {10}^{-3}atm$ $c{m}^3{g}^{-1}$

$=iRT\frac{L.atm}{mol}\frac{1d{m}^3}{L}{\left(\frac{10cm}{1dm}\right)}^3\frac{1}{M}\frac{mol}{g}$

$=\frac{1000iRT}{M}$

where $M$ is the molar mass in g/mol.

If $i\simeq 1$ for insulin, $T=27+273.15=300.15$

$M=\frac{1000iRT}{slope}$

$=\frac{1000\times 1\times 0.082057\times 300.15}{4.1\times {10}^{-3}}$

$=6.0\times {10}^{3}g$

Hence, te correct option is $\text{A}$