Osmotic Pressure — Revision Notes

⚡ 30-Second Revision

Osmosis: — Solvent flow through SPM from high solvent conc. to low solvent conc.
Osmotic Pressure (\(\Pi\)): — Pressure to stop osmosis. Colligative property.
Van't Hoff Equation: — \(\Pi = iCRT\)

- \(i\): Van't Hoff factor (1 for non-electrolytes, >1 for electrolytes) - \(C\): Molar concentration (mol/L) - \(R\): Gas constant (0.0821 L atm mol\(^{-1}\) K\(^{-1}\) or 8.314 J mol\(^{-1}\) K\(^{-1}\)) - \(T\): Absolute temperature (K)

Isotonic Solutions: — Equal \(\Pi\) (equal \(iC\) values).
Hypotonic: — Lower \(\Pi\) than cell \(\rightarrow\) cell swells.
Hypertonic: — Higher \(\Pi\) than cell \(\rightarrow\) cell shrinks.
Molar Mass Determination: — \(M = \frac{i w RT}{\Pi V}\)

2-Minute Revision

Osmotic pressure (\(\Pi\)) is a colligative property, meaning it depends on the number of solute particles, not their identity. It's the pressure required to stop osmosis, which is the net movement of solvent through a semi-permeable membrane (SPM) from a region of higher solvent concentration to lower solvent concentration.

The key formula is the Van't Hoff equation: \(\Pi = iCRT\). Here, \(i\) is the Van't Hoff factor (1 for non-electrolytes like glucose, >1 for electrolytes like NaCl (i=2) or \(CaCl_2\) (i=3)), \(C\) is the molar concentration in mol/L, \(R\) is the gas constant (0.

0821 L atm mol\(^{-1}\) K\(^{-1}\)), and \(T\) is the absolute temperature in Kelvin. Remember to convert \(^\circ\)C to K by adding 273. Isotonic solutions have the same osmotic pressure, meaning their \(iC\) values are equal.

This concept is vital in biology: hypotonic solutions cause cells to swell, hypertonic solutions cause them to shrink, and isotonic solutions maintain cell integrity. Osmotic pressure is particularly useful for determining the molecular masses of large molecules like proteins because it yields measurable values even for very dilute solutions at room temperature.

5-Minute Revision

Osmotic pressure (\(\Pi\)) is one of the four colligative properties, defined as the minimum pressure needed to prevent the net flow of solvent into a solution across a semi-permeable membrane. This phenomenon, osmosis, is driven by the tendency to equalize solvent chemical potential. The quantitative relationship is given by the Van't Hoff equation: \(\Pi = iCRT\).

Key components to remember:

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\(i\) (Van't Hoff factor): — Accounts for dissociation/association. For non-electrolytes (e.g., urea, glucose), \(i=1\). For electrolytes, count the ions: NaCl (\(i=2\)), \(CaCl_2\) (\(i=3\)), \(Al_2(SO_4)_3\) (\(i=5\)).
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\(C\) (Molar concentration): — Always in mol/L. If given in % (w/v), convert to molarity. E.g., 5% (w/v) glucose means 5g glucose in 100mL solution.
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\(R\) (Gas constant): — Use 0.0821 L atm mol\(^{-1}\) K\(^{-1}\) if pressure is in atm and volume in L. Use 8.314 J mol\(^{-1}\) K\(^{-1}\) if pressure is in Pa and volume in m\(^3\).
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\(T\) (Absolute temperature): — Always in Kelvin (K). Add 273 to \(^\circ\)C.

Applications and Concepts:

Molar Mass Determination: — \(\Pi = \frac{i w RT}{M V}\). This is especially useful for macromolecules (proteins, polymers) because \(\Pi\) is significant even for dilute solutions and can be measured at room temperature, preventing denaturation.
Isotonic, Hypotonic, Hypertonic Solutions: — Crucial for biological systems. Isotonic solutions have equal \(\Pi\) (e.g., 0.9% NaCl for blood). Hypotonic solutions have lower \(\Pi\) (water enters cells, causing swelling/bursting). Hypertonic solutions have higher \(\Pi\) (water leaves cells, causing shrinking).
Reverse Osmosis: — Applying pressure greater than \(\Pi\) to force solvent from solution to pure solvent, used in desalination.

Worked Example: Calculate the osmotic pressure of a 0.2 M \(MgCl_2\) solution at 27 \(^\circ\)C. (R = 0.082 L atm mol\(^{-1}\) K\(^{-1}\))

Step 1: — Determine \(i\) for \(MgCl_2\). \(MgCl_2 \rightarrow Mg^{2+} + 2Cl^-\). So, \(i=3\).
Step 2: — Convert \(T\) to Kelvin. \(T = 27 + 273 = 300\) K.
Step 3: — Apply \(\Pi = iCRT\).

\(\Pi = 3 \times 0.2 \text{ mol/L} \times 0.082 \text{ L atm mol}^{-1}\text{ K}^{-1} \times 300 \text{ K}\) \(\Pi = 14.76\) atm.

Remember to always check units and the Van't Hoff factor carefully.

Prelims Revision Notes

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Definition: — Osmotic pressure (\(\Pi\)) is the minimum pressure to prevent osmosis. It's a colligative property, depending only on the number of solute particles.
2
Osmosis: — Net movement of solvent through a semi-permeable membrane (SPM) from higher solvent concentration (lower solute concentration) to lower solvent concentration (higher solute concentration).
3
Van't Hoff Equation: — \(\Pi = iCRT\)

* \(i\): Van't Hoff factor. For non-electrolytes (glucose, urea), \(i=1\). For electrolytes, \(i\) = number of ions produced (e.g., NaCl \(i=2\), \(CaCl_2 \(i=3\), \(Al_2(SO_4)_3 \(i=5\)). * \(C\): Molar concentration (mol/L).

Calculate from given mass and volume: \(C = \frac{\text{mass}}{\text{Molar mass} \times \text{Volume (L)}}\). * \(R\): Gas constant. Use 0.0821 L atm mol\(^{-1}\) K\(^{-1}\) for \(\Pi\) in atm. Use 8.

314 J mol\(^{-1}\) K\(^{-1}\) for \(\Pi\) in Pa. * \(T\): Absolute temperature in Kelvin (K). \(T(\text{K}) = T(\text{^\circ C}) + 273\).

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Isotonic Solutions: — Solutions with the same osmotic pressure. If two solutions are isotonic, then \(i_1C_1 = i_2C_2\).
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Hypotonic Solution: — Lower osmotic pressure than a cell's cytoplasm. Water enters the cell, causing it to swell (hemolysis for RBCs).
3
Hypertonic Solution: — Higher osmotic pressure than a cell's cytoplasm. Water leaves the cell, causing it to shrink (crenation for RBCs).
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Molar Mass Determination: — Osmotic pressure is excellent for determining the molar masses of macromolecules (proteins, polymers) because:

* It gives large, easily measurable values even for very dilute solutions. * Measurements are done at room temperature, which is suitable for biomolecules. * Formula: \(M = \frac{i w RT}{\Pi V}\), where \(w\) is mass of solute.

1
Reverse Osmosis: — Process of forcing solvent through an SPM from a concentrated solution to a dilute solution by applying pressure greater than the osmotic pressure. Used in desalination.
2
Common Errors: — Incorrect 'i' value, not converting temperature to Kelvin, errors in molarity calculation (especially mL to L conversion), and confusing osmosis with diffusion.

Vyyuha Quick Recall

Please Include Concentration Really Thoroughly! \(\Pi = iCRT\)

Please: \(\Pi\) (Osmotic Pressure)
Include: \(i\) (Van't Hoff factor)
Concentration: \(C\) (Molar concentration)
Really: \(R\) (Gas constant)
Thoroughly: \(T\) (Absolute Temperature)