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# Osmotic Pressure

The functioning of the kidneys, sweating, dew drops and natural phenomenon like extracting pure water from the sea, industrial extractions and purification are based on the process called osmosis. In general terms, we can describe osmosis as a selective separation phenomenon.

Osmosis is defined as the phenomenon of the passage of solvent but not the solute through a semi permeable membrane from solvent to solution or from weak solution to concentrated solution.

The semi permeable membrane is a material which allows only the solvent to pass through but not the solute. Pig’s bladder, cell walls and parchment membrane are natural semi permeable membranes. Gelatinous salts like cupric ferrocyanide, Prussian blue, calcium phosphate are some of the synthetic semi permeable membranes.

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## Osmotic Pressure Definition

Osmotic pressure is defined as "the excess pressure that needs to be applied to a solution to prevent osmosis when a solution is separated from the solvent by a semi permeable membrane. It is usually denoted by ‘π'."

Different solutions having the same osmotic pressure at a particular temperature are called Isotonic solutions. Another Osmotic pressure definition is the hydrostatic pressure of the liquid column which prevents further inward penetration of more solvent through semi permeable membrane.

## Colligative Properties Osmotic Pressure

For a given solvent, the osmotic pressure depends only upon the molar concentration of the solute but does not depend on its nature.

The following relation relates osmotic pressure to the number of moles of a solute

PV = nRT Van't Hoff 's solution equation (p = Osmotic pressure)

or

$\pi = \frac{n}{v}RT$

but,

$\frac{n}{v} = C$

Therefore,

P = CRT

where,
C = Concentration of the solution in moles per liter
R = Gas constant
T = Temperature
n = Number of moles of the solute
v = Volume of the solution in liters

## Osmotic Pressure Equation

$\pi = h \times d \times g$

Where, h is the height of the liquid column, d is the density and g is the acceleration due to gravity.

This is considered as the osmotic pressure formula to calculate all related dynamics of osmotic pressure.

Principle of measuring osmotic pressure

If two solutions of an identical composition but different concentration are separated by a semi permeable membrane (one that permits only the solvent to pass through it), the direction of flow will be from the more dilute to the more concentrated solution (left to right in the illustration). This flow will continue until the hydrostatic pressure is developed at the concentrated solution front. This pressure prevents the further movement of solvent molecules. This pressure is called as osmotic pressure.

Osmosis is defined as the passage of solvent from pure solvent or from a solution of lower concentration into a solution of higher concentration through a semi-permeable membrane.

The osmotic pressure of a solution at a particular temperature may be defined as the excess hydraulic pressure that builds up when the solution/conc.solution is separated from the solvent/dil. solution by a semi permeable membrane.

## Osmotic Pressure Formula

### Vant Hoff 's Laws of Osmotic Pressure

Vant Hoff, analyzing the available data on osmotic pressure of solutions concluded that osmotic pressure of dilute solutions varied with their concentration and temperature in the same way as the pressure of the gas.

### Vant Hoff Boyles Law

He enunciated some laws for solutions which are parallel to those relating to gases. Osmotic pressure (p) of a solution at a constant temperature is directly proportional to its concentration C (i.e., moles per liter)

$\pi \propto C$

$\pi \propto$ $\frac{n}{v}$

where n is the number of moles of solute present in volume V liters of solution.

### Vant Hoff Charles Law

For a solution of fixed concentration, the osmotic pressure (p) of a solution is directly proportional to its absolute temperature (T).

$\pi \propto T$

Combining both the laws,

$\pi \propto$ $\frac{nT}{v}$

The constant of proportionality also turns out to be the same as gas constant R. Thus, $\pi$ = $\frac{n\ R\ T}{v}$

## How to Calculate Osmotic Pressure

Berkley and Hartley's apparatus

The apparatus consists of a strong steel vessel into which a porous pot is fitted. The walls of the porous pot are coated with copper ferrocyanide. Due to osmosis water moves into the steel vessel from the porous pot. The water level falls in the indicator tube. This can be stopped by applying pressure using the plunger. The pressure applied is equal to the osmotic pressure. This can be recorded using a pressure gauge.

### Solved Examples

Question 1: Calculate the osmotic pressure of a solution at a constant temperature of 270C. One litre of this solution contains 3 g. of a non electrolytic solute of molecular weight 60.
Solution:

Since the volume is given in litres, the pressure can be calculated in atmospheres. The value of gas constant R is therefore 0.082 L.atm per degree.

Applying equation,
$\pi$ = $\frac{1}{v}\times \frac{m}{M}\times$ $RT$ $\frac{3}{60}$ $\times 0.082\times (273+27)$
$\pi$ = 1.23 atmospheres.

Question 2: 100 mL of 3.4% urea solution and 100 mL of 1.8% solution of cane sugar is mixed thoroughly to form a uniform solution. Calculate the Osmotic pressure of this solution at 200C?
Solution:

Molecular weight of Urea [CO(NH2)2] = 60.
Molecular weight of Cane sugar (C12 H22 O11) = 342.
Total volume of solution after mixing = 200 mL
The mass (m) of urea in 1 L of this mixture will be 3.4 X 1000/200 = 17 g.
The mass of cane sugar in 1L of this mixture = 1.8 X 1000/200 = 9 g.

Osmotic pressure of Urea = $\pi$(urea) =$\frac{1}{v}\times \frac{m}{M}\times$ $RT$ $\frac{17}{60}$ $\times 0.082\times (273+20)$ = 6.8 atmospheres.

Osmotic pressure of Cane sugar = $\pi$(cane sugar) = $\frac{1}{v}\times \frac{m}{M}\times$ $RT$ $\frac{9}{6342}$ $\times 0.082\times 293$ = 0.63 atmospheres.

Since, in dilute solutions solutes behave like gases and obey gas laws, to get total pressure we can apply Dalton’s laws of partial pressures. Thus

Total Osmotic pressure π(solution) = $\pi$ (urea) + $\pi$ (cane sugar)
= 6.8 + 0.63 = 7.43 atmospheres.

## Determination of Molecular Mass from Osmotic Pressure

In order to determine the molecular mass of an unknown, non volatile compound, a known mass (say w g) of the compound is dissolved to prepare a known volume (say v liters) of solution. The osmotic pressure of the solution is determined and the molar mass is calculated as follows.

$\pi$ = $\frac{nB}{v}$$RT$

where nB is the number of moles of the solute and is given by WB/MB.

Hence WB is the mass of the solute in gm and MB is the molecular mass of the solute.

Thus,

$\pi$ = $\frac{W_{B}RT}{M_{B}V}$

$M_{B}$ = $\frac{W_{B}RT}{\pi V}$

This method is exceptionally suitable for the determination of molecular masses of macromolecules such as proteins and polymers. This is because, for these substances the values of other colligative properties such as elevation in boiling point or depression in freezing point are too small to be measured. On the other hand, osmotic pressure of such substances are measurable.