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Osmotic Pressure

200 cm3 on an...

Question

$200 c m^{3}$ on an aqueous solution contains $1.2 g$ of a polymer. The osmotic pressure of such solution at $300 K$ is found to be $2 \times 10^{- 3} a t m$ . What will be the molar mass of the polymer ?

73.9 k g m o l^{- 1}

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25.6 k g m o l^{- 1}

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0.87 k g m o l^{- 1}

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46.6 k g m o l^{- 1}

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Solution

The correct option is A $73.9 k g m o l^{- 1}$
Osmotic pressure:

$π = \frac{n}{V} \times R T$

Here n is number of moles

$n = \frac{Given mass}{Molar mass} = \frac{w_{B}}{m_{B}}$

$V = 200 c m^{3} = 0.2 L R = 0.0821 L a t m m o l^{- 1} K^{- 1}$

$\Rightarrow π V = \frac{w_{B}}{m_{B}} \times R T m_{B} = \frac{w_{B} \times R \times T}{π \times V}$

$m_{B} = \frac{1.2 g \times 0.0821 L a t m m o l^{- 1} K^{- 1} \times 300 K}{2 \times 10^{- 3} a t m \times 0.2 L} m_{B} = 73890 g m o l^{- 1} m_{B} = 73.89 k g m o l^{- 1}$

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