# Laws of Osmotic Pressure

## Laws of Osmotic Pressure

From a study of the experimental results obtained by Pfeffer, van't Hoff showed that for dilute solutions-

A. The osmotic pressure of a solution at a given temperature is directly proportional to its concentration.

B. The osmotic pressure of a solution of a given concentration is directly proportional to the absolute temperature.

From the above findings, van't Hoff IN 1877 established the laws of osmotic pressure and pointed out that these were closely related to the gas laws.

### Boyle-van't Hoff Law for Solutions

If π is the osmotic pressure and C its concentration, from (a) we can write π ∝ C, if temperature is
constant.

If the concentration of the solute is expressed in moles per litre and V is the volume of the solution that contains 1 mol of solute-

C = 1/V

Thus, π ∝ 1/V at constant temperature

This relationship is similar to the Boyle's law for gases and is known as the Boyle-van't Hoff law for solutions.

### Charles-van't Hoff Law for Solutions

If T is the absolute temperature, from the statement (B), we can write-

π ∝ T, if temperature is constant
This relationship is similar to the Charles' Law for gases and is known as Charles-van't Hoff law for solutions.

### Van't Hoff Equation for Solutions

As shown above the osmotic pressure (π) of a dilute solution is inversely proportional to the volume (V) containing 1 mole of the solute and is directly proportional to the absolute temperature (T).

This is,

π ∝ 1/V

π ∝ T

Combining the above two equations, van't Hoff gave the general relationship-

π V = R' T

where R' is a constant. He showed that this equation was parallel to the general Gas Equation (PV = RT), as the value of R' calculated from the experimental values of π, V, and T came out to be almost the same as of the Gas constant (R).

If n moles of solute are dissolved in V litres of solution, the above equation become-

π V = n R T

### Avogadro-van't Hoff Law for Solutions

Writing Van't Hoff equation for two different dilute solutions-

π_{1}V_{1} = n_{1}RT_{1}

π_{2}V_{2} = n_{2}RT_{2}

where n_{1} and n_{2} are the number of moles (molecules) of the solute in V_{1} and V_{2} litres of the two
solutions.

If π_{1} = π_{2} and T_{1} = T_{2}

Then from above two equations-

n_{1}/V_{1} = n_{2}/V_{2}

Hence __when osmotic pressure and temperature are the same, equal volumes of solutions would contain equal number of moles (molecules) of the solute__. This relationship is analogous to Avogadro's law of gases and is referred to as Avogadro-van't Hoff law for solutions. Alternatively, this law may be stated as: __Isotonic solutions at the same temperature have equimolar concentrations__.

## Limitations of Laws of Osmotic Pressure

Laws of osmotic pressure are not perfectly obeyed in following conditions-

1. If the solute is electrolyte.

2. If the solution is concentrate relatively.

3. If the solute is volatile.

4. If solute associates in the solution.

## Osmotic Pressure

When two solutions are separated by a semipermeable membrane, there is a spontaneous flow of the solvent from low to high concentration due to osmosis. The pressure that must be applied on the solution of higher concentration to prevent the low of the solvent from the solution of lower concentration is called is called osmotic pressure of the solution. It is denoted by π

We can determine the Osmotic pressure with the help of the following formula-

π = i × C × R × T
where,

i is van't Hoff factor.

C is molar concentration of the solute in the given solution.

R is universal gas constant.

T is temperature on the Kelvin scale.