Osmosis, Osmotic Pressure, and Reverse Osmosis

Have you ever noticed how raw mangoes shrivel up when you drop them into a jar of salty brine? Or how wilted flowers perk right back up when you place them in fresh water? These everyday observations all have one thing in common: water is moving through a barrier that lets it pass while holding back other substances. This process is called osmosis, and understanding it unlocks one of the most powerful colligative properties, one that scientists routinely use to weigh giant molecules like proteins.

Membranes That Pick and Choose: Semipermeable Membranes

The barrier behind osmosis is a special type of membrane. Look closely at cell walls, pig bladders, parchment, or synthetic films like cellophane, and they all share the same feature: they appear solid, but they are actually riddled with a network of tiny, submicroscopic pores.

These pores are large enough for small molecules (like water) to slip through, but too narrow for bigger molecules (like sugar or protein) to pass. A membrane with this selective property is called a semipermeable membrane (SPM) (a membrane that allows the passage of solvent molecules but blocks solute molecules).

Both natural and synthetic semipermeable membranes exist:

Natural membranes come from animal or plant tissue, such as pig’s bladder or parchment
Synthetic membranes like cellophane are manufactured for laboratory and industrial use

What Is Osmosis?

Picture a simple experiment. Take a semipermeable membrane and use it to separate pure water (on one side) from a sugar solution (on the other side). What happens?

The water molecules, being small enough to pass through the pores, begin flowing from the pure solvent side into the solution side. This spontaneous movement of solvent molecules through a semipermeable membrane, from a region of lower solute concentration towards higher solute concentration, is called osmosis.

Fig 1.9: Osmosis demonstrated with a thistle funnel. The wide mouth is sealed with a semipermeable membrane and dipped in pure solvent. As solvent flows into the solution by osmosis, the liquid level rises in the narrow stem to height h, producing osmotic pressure $\Pi = h\rho g$ .

Figure 1.9 shows a classic setup. An inverted thistle funnel has its wide mouth sealed with a semipermeable membrane and filled with solution. The funnel is then dipped into a beaker of pure solvent. Over time, solvent flows through the membrane into the solution, and the liquid level inside the narrow stem of the funnel rises. This rise continues until equilibrium is reached.

One critical point to remember: solvent molecules always flow from the side with lower solute concentration to the side with higher solute concentration. If you place a dilute solution on one side and a concentrated solution on the other, the solvent still flows towards the more concentrated side.

Osmotic Pressure: Stopping the Flow

You can stop osmosis by applying extra pressure on the solution side, pushing back against the incoming solvent. The exact amount of pressure needed to completely halt the flow of solvent through the membrane is called the osmotic pressure of the solution.

Fig 1.10: Preventing osmosis. When a pressure equal to the osmotic pressure ( $\Pi$ ) is applied on the solution side (in addition to atmospheric pressure), the net flow of solvent through the semipermeable membrane drops to zero.

Think of it this way: the solution naturally “pulls” solvent towards itself through osmosis. Osmotic pressure is the counter-push you need to apply to exactly cancel that pull.

Since osmotic pressure depends on how many solute particles are dissolved (not on what they are), it is a colligative property, just like vapour pressure lowering, boiling point elevation, and freezing point depression.

The Van’t Hoff Equation: Quantifying Osmotic Pressure

Experiments with dilute solutions reveal that osmotic pressure follows a beautifully simple relationship. It is directly proportional to the molarity ( $C$ , in mol/L) of the solution at a given temperature:

$\Pi = C \, R \, T \qquad \text{(1.39)}$

Here:

$\Pi$ is the osmotic pressure (in bar or atm)
$C$ is the molar concentration of the solute (mol/L)
$R$ is the gas constant (0.083 L bar $mol^{-1}$ $K^{-1}$ , or 0.0821 L atm $mol^{-1}$ $K^{-1}$ )
$T$ is the absolute temperature (in K)

Notice something remarkable: this equation has exactly the same form as the ideal gas equation $PV = nRT$ , rearranged as $P = (n/V)RT = CRT$ . This is not a coincidence; it reflects a deep connection that Van’t Hoff recognised between the behaviour of dilute solutions and ideal gases.

From Concentration to Moles and Mass

Since molarity equals the number of moles of solute divided by the volume of solution in litres, we can write $C = n_2 / V$ , which gives:

$\Pi = \frac{n_2}{V} \, R \, T \qquad \text{(1.40)}$

Multiplying both sides by $V$ :

$\Pi \, V = n_2 \, R \, T$

Now, the number of moles of solute can be written as $n_2 = w_2 / M_2$ (mass of solute divided by its molar mass). Substituting:

$\Pi \, V = \frac{w_2 \, R \, T}{M_2} \qquad \text{(1.41)}$

Rearranging to solve for the molar mass:

$M_2 = \frac{w_2 \, R \, T}{\Pi \, V} \qquad \text{(1.42)}$

This is extremely useful. If you measure the osmotic pressure ( $\Pi$ ) of a solution containing a known mass ( $w_2$ ) of solute in a known volume ( $V$ ) at temperature $T$ , you can directly calculate the molar mass of the solute.

Why Osmotic Pressure Wins for Big Molecules

The osmotic pressure method offers several practical advantages over other colligative property methods (boiling point elevation or freezing point depression) for finding molar masses:

Room temperature measurement : pressure is measured near room temperature, so heat-sensitive biomolecules like proteins are not destroyed
Large measurable values : even very dilute solutions of high-molar-mass solutes produce a measurable osmotic pressure, whereas the boiling point elevation or freezing point depression for the same solution might be too tiny to detect reliably
Uses molarity, not molality : molarity is easier to work with experimentally, since you simply dissolve a known mass in a measured volume of solution
Perfect for macromolecules : proteins, polymers, and other macromolecules often have poor solubility (giving only dilute solutions) and are unstable at high temperatures, making the osmotic pressure method the natural choice

This is why the osmotic pressure technique is widely used in biochemistry and polymer science for molar mass determination.

Worked Example: Finding the Molar Mass of a Protein (Example 1.11)

Problem: 200 $cm^3$ of an aqueous solution contains 1.26 g of a protein. The osmotic pressure of this solution at 300 K is found to be $2.57 \times 10^{-3}$ bar. Calculate the molar mass of the protein.

Solution:

First, list all the known quantities:

$w_2 = 1.26$ g (mass of protein)
$V = 200 \, cm^3 = 0.200$ L (volume of solution, converted to litres)
$T = 300$ K
$\Pi = 2.57 \times 10^{-3}$ bar
$R = 0.083$ L bar $mol^{-1}$ $K^{-1}$

Now apply Equation 1.42:

$M_2 = \frac{w_2 \, R \, T}{\Pi \, V}$

Substitute the values:

$M_2 = \frac{1.26 \times 0.083 \times 300}{2.57 \times 10^{-3} \times 0.200}$

Calculate the numerator:

$1.26 \times 0.083 = 0.10458$

$0.10458 \times 300 = 31.374$

Calculate the denominator:

$2.57 \times 10^{-3} \times 0.200 = 5.14 \times 10^{-4}$

Divide:

$M_2 = \frac{31.374}{5.14 \times 10^{-4}} = 61{,}022 \text{ g } mol^{-1}$

A molar mass of about 61,000 g $mol^{-1}$ is typical for a protein. This large value makes sense because proteins are macromolecules built from hundreds of amino acid units linked together.

Matching Osmotic Pressures: Isotonic, Hypertonic, and Hypotonic Solutions

When dealing with living cells, the osmotic pressure of the surrounding fluid matters enormously. Three terms describe the relationship between a solution and the fluid inside cells:

Isotonic solutions (equal osmotic pressure) : two solutions with the same osmotic pressure at a given temperature are called isotonic. When separated by a semipermeable membrane, no net osmosis occurs between them. For human blood cells, a 0.9% (mass/volume) $NaCl$ solution, called normal saline, is isotonic with the intracellular fluid. This is why normal saline is safe for intravenous injection.
Hypertonic solutions (higher osmotic pressure) : a solution with a solute concentration greater than 0.9% $NaCl$ (relative to blood) is hypertonic. If blood cells are placed in a hypertonic solution, water flows out of the cells by osmosis, and the cells shrink.
Hypotonic solutions (lower osmotic pressure) : a solution with a solute concentration less than 0.9% $NaCl$ is hypotonic. Cells placed in a hypotonic solution absorb water by osmosis and swell. If the swelling is excessive, the cells may burst.

Osmosis in Everyday Life

The phenomena mentioned at the start of this topic are all explained by osmosis:

Pickling with salt : raw mangoes placed in concentrated brine lose water through osmosis and shrivel into pickles. The brine is hypertonic relative to the mango cells.
Reviving wilted flowers : placing wilted flowers in fresh water allows water to enter the cells by osmosis (the fresh water is hypotonic relative to the cell sap), restoring the cells’ turgidity and making the flowers look fresh again. A limp carrot placed in water firms up by the same mechanism.
Blood cell behaviour : placing blood cells in water containing less than 0.9% salt causes swelling as water enters by osmosis.
Salt-induced water retention (edema) : people who consume large amounts of salt may experience puffiness or swelling in tissues. The high salt concentration in intercellular spaces draws water out of cells and blood vessels by osmosis, and this accumulated water causes the swelling known as edema (abnormal fluid retention in body tissues).
Water movement in plants : water travels from the soil into root cells and then upward through the plant partly by osmosis. The soil water is hypotonic compared to the cell sap inside root cells, so water flows inward.
Food preservation : salting meat or adding sugar to fruits creates a hypertonic environment on the food surface. Bacteria landing on such food lose water by osmosis, shrivel, and die, protecting the food from spoilage.

Reverse Osmosis: Turning the Flow Around

In normal osmosis, solvent flows spontaneously from the pure solvent side into the solution. But what if you could force it to go the other way, pushing pure solvent out of the solution?

You can, by applying a pressure on the solution side that is greater than its osmotic pressure. Under this extra pressure, the natural direction reverses: pure solvent is squeezed out of the solution through the semipermeable membrane, leaving the solute behind. This is called reverse osmosis.

Fig 1.11: Reverse osmosis. When a pressure exceeding the osmotic pressure is applied to the salt water side via a piston, pure fresh water is forced through the semipermeable membrane and collected on the other side.

Desalination: Making Sea Water Drinkable

The most important application of reverse osmosis is the desalination (removal of dissolved salts from) sea water to produce fresh, potable (drinkable) water.

In a reverse osmosis desalination plant:

Sea water is pumped against a semipermeable membrane at high pressure (greater than the osmotic pressure of sea water)
Pure water passes through the membrane and is collected as fresh water
The dissolved salts and impurities remain on the high-pressure side and are discarded

A common membrane material is cellulose acetate, a polymer film that is permeable to water molecules but blocks dissolved salts and other impurities. These membranes are placed over a suitable porous support structure to withstand the high pressures involved.

Many countries around the world now rely on reverse osmosis desalination plants to meet their drinking water requirements, especially in arid regions where fresh water is scarce.