Osmotic Pressure

CHEColligative Properties

Osmotic pressure is the colligative property best suited to macromolecules because it gives large, measurable values even at tiny concentrations. ISC questions ask for $\pi$ , molar mass from $\pi$ , and the definitions of isotonic, hypertonic and hypotonic solutions.

Osmotic pressure (van't Hoff equation)

\pi = i C R T = i\,\dfrac{n}{V}\,R T

C

molarity,

R = 0.0821

L atm K

^{-1}

mol

^{-1}

T

in kelvin

Molar mass from osmotic pressure

M = \dfrac{i\, w \, R \, T}{\pi \, V}

w

solute mass (g),

V

solution volume (L),

\pi

in atm (

i = 1

for a non-electrolyte)

Isotonic condition

\pi_1 = \pi_2 \quad\Rightarrow\quad (iC)_1 = (iC)_2

equal osmotic pressure at the same temperature

Osmotic pressure $\pi = iCRT$ , where $C = \dfrac{n}{V}$ is molarity; use $R = 0.0821\,\text{L atm K}^{-1}\text{mol}^{-1}$ and $T$ in kelvin.
Molar mass from osmotic pressure: $M = \dfrac{i \, w \, R \, T}{\pi \, V}$ , with $w$ the solute mass and $V$ the solution volume in litres ( $i = 1$ for an unknown non-electrolyte such as a polymer or protein).
Isotonic solutions have equal $\pi$ (no net flow); a cell placed in a hypertonic solution (higher $\pi$ ) loses water and shrinks/crenates, while in a hypotonic solution (lower $\pi$ ) it gains water and swells/bursts.
Equal osmotic pressure means equal $iC$ : e.g. for two non-electrolytes, equal $\pi$ requires equal molar concentrations.
Preferred for polymers and proteins because even a small concentration produces a sizeable, accurately measurable pressure, and measurements are made at room temperature (no risk of decomposition).
Reverse osmosis: applying pressure greater than $\pi$ forces solvent backwards through a semi-permeable membrane — the basis of desalination.
Osmosis is the net flow of solvent (not solute) through a semi-permeable membrane from the dilute to the concentrated side; osmotic pressure is the external pressure that just stops this flow.
$0.9\%$ $NaCl$ saline and $5\%$ glucose are isotonic with blood, so red blood cells neither swell nor shrink in them — the standard physiological example.
Because $\pi \propto iC$ , ionic solutes exert a larger osmotic pressure than a non-electrolyte of the same molarity by the factor $i$ .
Osmotic pressure is large (atmospheres) compared with the tiny $\Delta T_f$ or $\Delta T_b$ that the same dilute solution would give, which is why it is the most sensitive colligative method for large molar masses.
Trap: $C$ in $\pi = iCRT$ is molarity (mol per litre of solution), so convert volumes given in mL to litres before computing.

Where the marks go

Forgetting to convert the volume from mL to L (or temperature from $^\circ$ C to K) before applying $\pi = iCRT$ .
Dropping the van't Hoff factor for an electrolyte, which underestimates $\pi$ by the factor $i$ .
Reversing the direction of osmosis — solvent flows toward the more concentrated (higher $\pi$ ) solution, and a cell in a hypertonic medium loses water.
Using the wrong value or units of $R$ ; with $\pi$ in atm use $R = 0.0821$ , not the SI $8.314$ .
Confusing isotonic (equal $\pi$ ), hypertonic (greater $\pi$ ) and hypotonic (lower $\pi$ ) relative to the reference solution.

How the board asks it

Numericalvan't Hoff equation $\pi = iCRT$
Calculate the osmotic pressure of a solution containing $3.42\,\text{g}$ of sucrose ( $M = 342\,\text{g mol}^{-1}$ ) dissolved in $250\,\text{mL}$ of solution at $27^\circ\text{C}$ ( $R = 0.0821\,\text{L atm K}^{-1}\text{mol}^{-1}$ ).
Numericalmolar mass from osmotic pressure
A solution containing $1.0\,\text{g}$ of a protein in $100\,\text{mL}$ of solution shows an osmotic pressure of $2.57 \times 10^{-3}\,\text{atm}$ at $300\,\text{K}$ . Calculate the molar mass of the protein ( $R = 0.0821\,\text{L atm K}^{-1}\text{mol}^{-1}$ ).
Define / stateisotonic, hypertonic and hypotonic solutions
Define the terms isotonic, hypertonic and hypotonic solutions, and state what happens to a red blood cell placed in a hypertonic solution.
Give reasonspreferred for polymers and proteins
Give a reason: osmotic pressure is preferred over the elevation of boiling point for determining the molar masses of polymers and proteins.
Predict the productnet flow governed by $iC$
A $0.1\,\text{M}$ solution of $NaCl$ and a $0.1\,\text{M}$ solution of glucose are separated by a semi-permeable membrane. Predict the direction of net solvent flow and give a reason.
Assertion–Reasonreverse osmosis and desalination
Assertion: Reverse osmosis is used for the desalination of sea water. Reason: When a pressure greater than the osmotic pressure is applied, solvent flows from the solution into the pure solvent through a semi-permeable membrane.

Practise this topic

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Written for Sublevo. Question text quoted anywhere in these notes is the Council’s and carries its year and paper; the board’s own diagrams are not reproduced.