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How will you determine molar mass of solute from osmotic pressure?

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Question

How will you determine molar mass of solute from osmotic pressure?

Derivation
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Solution

For very dilute solution, osmotic pressure is given by

πV = n2RT

where,

π = Osmotic pressure in atm.

V = Volume of a solution in dm3

n2 = Moles of non-volatile solute

R = Gas constant = 0.082L dm3 atm K−1mol−1

T = temperature in Kelvin

∴ `pi = (n_2RT)/V`

`pi = (W_2RT)/(M_2V)    ...[because n_2 = W_2/M_2]`

∴ `M_2 = (W_2 R T)/(pi V)`

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