# Osmotic Pressure: Determination and Applications

Osmotic pressure is one of the colligative properties of the solution. If two solutions at different concentrations are separated by a semi-permeable membrane, it allows only the solvent molecules to pass through, from a lower concentration to a higher one. This process is known as osmosis and the minimum pressure applied to stop the osmosis phenomenon is called, osmotic pressure.

Osmotic pressure is represented by the Greek letter “π” which is determined by Vant Hoff’s equation:

π = i.M.R.T

where,

• π = osmotic pressure
• i = Vant Hoff’s factor
• M = Molarity of solution (mol/L)
• R = General gas constant (0.0821 dm3atm mol-1K-1)
• T = Temperature (K)

Working principle of Osmotic pressure

It works on the principle of diffusion in water. Two solutions at different concentration levels try to equalize their concentration due to the concentration gradient that develops on its own when there is a change in the concentration of something. The minimum pressure applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane is called osmotic pressure.

## Experimental demonstration

If a solution and its pure solvent are separated by a semipermeable membrane, the volume of the solution starts to rise. After a certain time, it will stop rising as the concentration gradient will now be zero. If a certain amount of pressure is applied on the solution end, it can stop the inward movement of pure solvent but the internal pressure on the solvent end will rise. This pressure, the pressure applied on the solution end, or the pressure rise seen on the solvent end is the osmotic pressure of this system. ## Methods to determine osmotic pressure

There are several methods to determine the osmotic pressure of a solution. Following are the names of those experimental methods.

• Pfeffer’s method
• Berkley and Hartley’s method
• Through modern technology osmometer

### Pfeffer’s method

Osmotic pressure can be determined by using the Pfeffer apparatus that was designed by Pfeffer in 1877. It consists of the following components:

1. A container: that contains the main assembly
2. Semipermeable membrane pot: It is made up of copper ferrocyanide perforated walls
3. A concentrated solution containing container: present on the other side of the semipermeable membrane
4. Sealed glass cover
5. Manometer
6. Scale The inside pot is filled with a solution containing the solvent present in the outside container. The main container usually has pure water. The inner pot is connected with a manometer at the zero mark. When water starts moving inside the solution due to osmotic pressure creating pressure on the manometer, it starts rising. The maximum height achieved by the manometer is the osmotic pressure of the given solution.

### Berkeley and hartley’s method

It is a more efficient method for the determination of osmotic pressure as an external pressure source is used to halt the moment of solvent in the solution. In the above figure, two interconnected tubes containing the pure solvent are present, passing through a solution contained inside the main body of the osmometer. When the osmosis process initiates the meniscus level connected with the solvent tube starts falling. The external pressure is then employed from the top of the solution tank to stop osmosis. The applied pressure is the required osmotic pressure of this solution.

### Modern Osmometer

It is an advanced instrument for the measurement of osmotic pressure. It is made up of a well-insulated metal cell which is divided into two compartments with a semipermeable membrane.

When a solution under investigation is added to the upper chamber, the solvent compartment is then connected with the diaphragm. The solvent starts flowing in through osmosis from the lower concentration region to a higher one. It applies a strain on the diaphragm which can be measured through a device called a strain gauge. The strain therefore produced is directly proportional to the osmotic pressure. The strain gauge is attached to an electronic device that produces a digital signal accordingly. Hence, the osmotic pressure is evaluated.

## Laws of osmotic pressure

By experimental results, it has been concluded that osmotic pressure for a dilute solution always obeys these laws:

Boyle-Vant Hoff’s law of solution

Osmotic pressure at a given temperature is directly proportional to the difference in the concentrations of two solutions.

Charles-Vant Hoff’s law of solution

Osmotic pressure is directly proportional to the temperature.

### Vant Hoff’s equation of osmotic pressure

The osmotic pressure is directly proportional to the concentration of a solution and inversely proportional to its volume.

From 1st law of osmotic pressure:

π C

{since C 1/V}

π 1/V      (i)

From the 2nd law of osmotic pressure,

π T      (ii)

By combining equations (i) & (ii)

π T/V

π.V T

π.V = R’ T      (iii)

where R’ is constant.

For “n” number of moles equation (iii) becomes,

π.V = n R’ T    or      π = M R’ T      (iv)

where,

“V” is the volume in m3

“T” is the temperature in kelvin

“M” is the molarity of the solution.

It can be seen that this equation is parallel to the General gas equation that is PV = nRT. It is observed from calculations that the value of the R’ constant is almost the same as the “R” gas constant having value of 8.36 J mol-1 K-1. However, the value of the gas constant is 8.31 J mol-1 K-1.

If two solutions “A” and “B”  are two dilute solutions, their Vant Hoff’s equation is given by;

For solution A

π1.V1 = n1 R’ T1      (v)

Similarly, for solution B

π2.V2 = n2 R’ T2      (vi)

If T1 = T2 and  π1 =  π2 , dividing equation (v) by (vi), we get

n1/n2 = V1/V2      (vii)

Equation (vii) is known as Vant Hoff’s – Avogadro’s law of solutions.

Example 1:

In an experiment, 20 grams of glucose with a molar mass of 180 g/mol is dissolved in 0.1 m3 of solution. If R’ is equal to 8.36 J mol-1 K-1, calculate the osmotic pressure by the Vant Hoff equation at room temperature.

Given data:

Volume  V = 0.1 m3

mass of solute = m = 20g

R’ = 8.36 J mol-1 K-1

Temperature T = 298 K

From Vant Hoff’s equation,

π.V = mass/molar mass x R’ T

π =  0.1 x (20/180) x 8.36 x 298

π = 27.5 Nm-2

## Relationship between Vapor pressure and Osmotic pressure

The osmotic pressure of the liquid is directly proportional to the lowering of vapor pressure. So, if P is the pressure of the solvent and Ps is the vapor pressure of the solution, the relationship between vapor pressure and osmotic pressure is given by:

π ∝ P – Ps

Relative lowering of vapor pressure is the relative change in pressure with respect to the added solute. It is always directly proportional to the osmotic potential produced in the solution.

π ∝ (P – Ps) / P

## Applications of Osmotic pressure

Osmotic pressure is a property of solutions that changes with changes in concentration and temperature. Therefore, it has many applications in analytic and the medical field, etc.

### Determination of Molar mass from Osmotic pressure

In general, measurement of osmotic pressure gives much more accurate molar mass than other colligative properties, such as elevation of boiling point, or lowering of freezing point. For this purpose, a known mass of unknown solute is added to the osmometer. Osmotic pressure obtained is employed to calculate molar mass. by the osmotic pressure formula:

π = i.M.R.T

Example:

To determine the molar mass of unknown salt, 1g of it is dissolved in a solvent to make 10 ml of solution. The osmometer shows that the osmotic pressure of this solution is 1.12 atm. Calculate the molar mass of the salt at 20 oC.

Given data:

Volume V =  10 cm3 or 0.01 dm3

mass of solute  m = 1g

R’ = 8.36 J mol-1 K-1

Temperature  T = 20 + 273 = 293 K

π = 1.12 atm = 1.12 x 101325 = 113484 Nm-2

Now,

π = M R’ T  ( Vant Hoff’s equation for solutions)

M = π / R’T

M = 1.12

### Preservation of food

In ancient times, people used to preserve food by placing it in a concentrated solution of sugar and salts. It gives hypertonic conditions to bacteria cells and they start losing water and eventually die. Common examples are marmalade and pickle.

### Osmotic pressure in plants

Osmotic pressure is important in maintaining the shape of leaves. The concentration of solute in leave cells is different from that in the atmosphere which provides the necessary rigidity to the leaves. When its equilibrium is disturbed, leaves tend to start wilting.

### Dialysis

A phenomenon similar to osmosis takes place in the cell walls of animals when nitrogenous waste materials are collected from all over the body. However, it allows the movement of solvent as small solute particles and does not allow large particles such as protein to pass through.

The application of dialysis in the medical field as an artificial kidney for the detoxification of blood is marvelous and life-saving. The tube containing the blood is immersed in the solution having the same molecules as blood at a low concentration called a washing solution. The blood from the patient circulates through a washing solution and due to the osmotic effect, solute particles from blood (at a higher concentration of waste salts) go into the washing solution. Hence, purification of the blood by expelling the unwanted (nitrogenous) molecules takes place.

### Reverse osmosis

When an aqueous solution (water containing impurities) is placed in a container with pure water separated by a semipermeable membrane (SPM), osmosis occurs. If the pressure greater than the osmotic pressure is applied the water (solvent) from the solution side starts moving towards pure water. In that case, SPM is functioning as a filter of microparticles such as salts and microbes. Therefore, reverse osmosis is used in water filtration plants, commonly called Reverse osmosis/RO plants.

## Concepts Berg

What is osmotic pressure?

It is pressure excited by the solvent at a low concentration towards a high concentration solution separated by a semipermeable membrane.

What are the units for osmotic pressure?

Osmotic pressure has the units of pressure:

• SI units: Pascal: Pa or Nm-2
• Atm: 1 atm is equal to 101325 Nm-2
• Pound per square inch (psi): 1 psi equals 14.7 Pa

How does osmotic pressure work?

When two solutions of the same solvent having different concentrations are separated through a porous membrane, osmosis occurs at the equilibrium concentration. The pressure applied to the concentrated solution to stop osmosis is osmotic pressure.

How is an osmotic pressure generated within a cell?

In a cell, osmotic pressure is generated when the concentration of the surrounding solution is different from the cell.

Why is osmotic pressure a colligative property?

Osmotic pressure is a colligative property. It obeys Raoult’s law which states that “The osmotic pressure of a solution is directly proportional to the added solute and relative lowering of vapor pressure”.

What are some real-life beautiful examples of osmotic pressure?

Some real-life examples are of osmotic pressure are:

• Transfer of water in a closed snail shell.
• The maintenance of the shape of leaves in plants.
• The kidney operates on the principle of osmosis.
• Uptake of food and water by plants.
• Preservation of food for example meat with sprinkled salt, etc.

What is the difference between osmolarity and osmotic pressure?

Osmolarity is the concentration of the solution, the cause of osmosis whereas, osmotic pressure is the required pressure to be exerted to halt osmosis.

What determines the rate of osmosis?

The rate of osmosis is directly proportional to the concentration difference between the two solutions undergoing osmosis.

Why is reverse osmosis used to desalinate water so expensive?

Reverse osmosis is expensive as it requires high-power electricity pumps. Furthermore, the semipermeable membrane is also made up of special material that comes very costly.

How do osmotic and hydrostatic pressure differ?

Hydrostatic pressure is the pressure exerted by the water on the walls of the container due to gravity, whereas, osmotic pressure is a colligative property of the solution.

Will osmotic dehydration in a sugar solution makes fruit taste sweeter?

Osmotic dehydration is the application of osmotic pressure. It is the method to store fruits for a longer time with osmotic agents. By virtue of this, taste, sweetness, and odor are enhanced.

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