Question

How is osmotic pressure of a solution determined ? If the membrane used was slightly leaky, how will it influence the measured value of osmotic pressure?
Osmotic pressure of a solution containing 7 g of a protein per 103 ml of solution is 25 mm Hg at 310 K. Calculate the molecular mass or the protein. (R = 0.0821 L atm K^–1 mol).

Solution

Answer:

Osmotic pressure: Osmotic pressure is the minimum pressure that should be applied to the more concentrated solution to prevent osmosis.
osmotic pressure is proportional to the molarity, C of the solution at a given temperature T. Thus: Π = C R T
Here Π is the osmotic pressure and R is the gas constant.

(a) Measurement of Osmotic Pressure. Different methods are employed for the measurement of osmotic pressure in the laboratory but Berkley and Hartley's method gives the best results. The apparatus consists of a porous pot containing copper ferrocyanide deposited in its wall (acts as semi-permeable membrane) and fitted into a bronze cylinder to which is fitted a piston and a pressure gauge (to read the applied pressure).

The pot is fitted with a capillary indicator on left and water reservoir on right. Pot is filled with water while the cylinder is filled with a solution whose osmotic pressure is to be measured. Water tends to pass into the solution through the semipermeable membrane with the result that the water level in the indicator falls down. External pressure is now applied with piston so as to maintain a constant level in the indicator. This external pressure is osmotic pressure.
If the membrane used was a slightly, leaky, then the measured valued of osmotic pressure will not be definite.

Fig. Berkley and Hartley's apparatus.
(b)
we have given that
m_B = 7g
R=0.0821 L atm K^-1 mol

$M_{B} = \frac{m_{B} RT}{Vπ} m = \frac{7 \times 0.0821 \times 310}{\frac{100}{1000} \times \frac{25}{760}} \times 54094 g {mol}^{- 1} .$

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