Osmosis

Osmosis is the net movement of solvent through a membrane that is much more permeable to solvent than to the dissolved solute. The direction is set by the solvent chemical potential, not by a mysterious force that “pulls water toward salt.”

A semipermeable membrane creates the situation

If solute cannot cross but solvent can, mixing cannot occur in the usual way. Solvent tends to move toward the side where its chemical potential is lower. For dilute solutions at equal temperature and pressure, that is usually the side with higher solute-particle concentration.

The membrane must distinguish solvent from solute. Without selective permeability, ordinary diffusion of both components changes the problem.

Osmotic pressure balances the tendency to flow

For an ideal dilute solution: π = iMRT

π is osmotic pressure, M molar concentration, T absolute temperature, and i accounts approximately for the number of dissolved particles produced per formula unit.

Osmotic pressure is the additional pressure that would have to be applied to the solution side to stop net solvent entry. It is a colligative property in the dilute ideal limit.

Osmotic-pressure explorer

M (mol L⁻¹) T (K) i

Pressure is the opposing thermodynamic variable. At equilibrium, the pressure difference offsets the solvent chemical-potential difference.

Tonicity is a biological application, not a synonym

In cells, what matters is whether solutes can cross the membrane over the relevant timescale. A solution can be iso-osmotic yet not isotonic if its solute rapidly enters the cell. Tonicity therefore depends on membrane permeability as well as concentration.

Real solutions depart from the ideal formula

The van ’t Hoff expression works best for dilute solutions. Electrolyte ions interact, molecules may associate, and membranes are rarely perfectly selective. For careful work, activities and measured osmotic coefficients replace the simple particle-counting approximation.

Worked examples

1. Sucrose osmotic pressure

Solution

For 0.20 M sucrose at 298 K with i≈1, π≈(0.20)(0.08206)(298)=4.89 atm.

2. Ideal NaCl comparison

Solution

At the same M and T, ideal NaCl with i≈2 gives roughly twice the osmotic pressure of a nonelectrolyte, though real solutions deviate.

3. Reverse osmosis

Solution

If a solution has π=25 bar, applying 30 bar to the solution side exceeds π, so net solvent flow can be driven opposite the spontaneous osmotic direction.