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Insulin is dissolved a suitable solvent and the osmotic pressure of( $π$ ) solutions of various concentration C (g/cc) is measured at 20°C . The slope of a plot of $π$ against C is $4.65 \times 10^{- 3} .$ Molecular weight of insulin is

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$3 \times 10^{5}$

$4.8 \times 10^{5}$

$5.23 \times 10^{5}$

$9 \times 10^{5}$

answer is D.

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Detailed Solution

$π = CRT$

$= \frac{n}{v} = RT = \frac{w_{A}}{W_{A} v} \times RT = (\frac{w_{A}}{v}) \frac{RT}{m_{A}}$

$∴ π = (\frac{RT}{m_{A}}) \frac{w}{v}$

y = mix + C , here C = 0

Given $m = 4.64 \times 10^{- 3}$

$\Rightarrow \frac{RT}{m_{A}} = 4.65 \times 10^{- 3}$

$\Rightarrow m_{A} = \frac{0.0821 \times 293}{4.65 \times 10^{- 3}}$

$= 5.17 \times 10^{3}$

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