Difficulty: Intermediate | Prerequisites: Redox reactions, mole concept, basic thermodynamics (Gibbs energy).
These two chapters (Electrochemistry Ch. 4, Solutions Ch. 2) share the idea that measurable physical quantities (cell potential, osmotic pressure, conductivity) connect to the number and behaviour of particles in solution. Together they carry roughly 8 marks on a CBSE paper.
TL;DR
Cell potential drives spontaneity (negative delta-G = spontaneous). The Nernst equation adjusts cell potential for non-standard concentrations. Osmotic pressure depends on the number of solute particles, not their identity (colligative property). Ionic solutes like KCl produce more particles and higher osmotic pressure than non-ionic solutes like urea at the same molarity.
Cell potential (Ecell)
The difference in electric potential between cathode and anode in an electrochemical cell. Ecell = Ecathode - Eanode. A positive Ecell means the reaction is spontaneous.
Standard Gibbs energy (delta-G0)
Related to cell potential by delta-G0 = -nFE0cell. A negative delta-G0 means spontaneous under standard conditions. n = moles of electrons transferred, F = 96500 C/mol (Faraday constant).
Nernst equation
Adjusts cell potential for non-standard conditions: Ecell = E0cell - (0.0592/n) x log([products]/[reactants]) at 25 degrees C.
Faraday constant (F)
96500 C/mol. The charge carried by one mole of electrons. The charge required for a redox half-reaction = n x F, where n is the number of electrons transferred.
Fuel cell
An electrochemical cell that converts chemical energy of a fuel (typically H2) directly into electrical energy. The only byproduct of a hydrogen fuel cell is water.
Molar conductivity (Lambda-m)
The conductivity of a solution divided by the molar concentration of the electrolyte. Measured in ohm-1 cm2 mol-1. It increases with dilution for all electrolytes.
Degree of dissociation (alpha)
The fraction of total solute molecules that dissociate into ions: alpha = Lambda-m / Lambda-m-0. For acetic acid, alpha is small (weak electrolyte).
Kohlrausch's law
At infinite dilution, the molar conductivity of an electrolyte equals the sum of the individual ionic conductivities: Lambda-m-0 = lambda-0(cation) + lambda-0(anion). Used to calculate Lambda-m-0 for weak electrolytes indirectly.
Osmotic pressure (pi)
The external pressure required to prevent osmosis. pi = nRT/V (or pi = CRT where C is molar concentration). It is a colligative property.
Colligative property
A solution property that depends only on the number of solute particles, not on their nature. The four colligative properties: relative lowering of vapour pressure, boiling-point elevation, freezing-point depression, osmotic pressure.
Isotonic solutions
Solutions with equal osmotic pressure. They contain the same number of moles of solute particles per unit volume.
Reverse osmosis
The process of forcing solvent from a concentrated solution through a semipermeable membrane to a dilute solution by applying pressure greater than the osmotic pressure. Used in water purification. A common SPM: cellulose acetate.
Reaction: Au(s) + Ca2+(1M) --> Au3+(1M) + Ca(s)
Given: E0(Au3+/Au) = +1.5 V, E0(Ca2+/Ca) = -2.87 V.
E0cell = E0cathode - E0anode = 1.5 - (-2.87) = 4.37 V
n = 3 (three electrons transferred per formula unit, balancing Au --> Au3+ and Ca2+ --> Ca)
delta-G0 = -nFE0 = -3 x 96500 x 4.37 = -1.26 x 10^6 J/mol
Since delta-G0 is negative, the reaction is spontaneous.
Cell: Zn(s) | Zn2+(0.1M) || Cd2+(0.01M) | Cd(s)
Given: E0(Zn2+/Zn) = -0.40 V, E0(Cd2+/Cd) = -0.76 V.
E0cell = E0cathode - E0anode = (-0.76) - (-0.40) = -0.36 V
n = 2
Ecell = -0.36 - (0.0592/2) x log(0.01/0.1) = -0.36 - 0.0296 x (-1) = -0.36 + 0.0296 = -0.33 V
Ag2S + 2e- --> 2Ag + S2- (E0 = -0.71 V, cathode)
Al3+ + 3e- --> Al (E0 = -1.66 V, reversed as anode)
E0cell = -0.71 - (-1.66) = 0.95 V (positive, so spontaneous)
Aluminium oxidises, reducing Ag2S back to metallic silver.
Calculate Lambda-m-0 for acetic acid and alpha, given Lambda-m = 48.1.
Using Kohlrausch's law: Lambda-m-0(CH3COOH) = Lambda-m-0(HCl) + Lambda-m-0(CH3COONa) - Lambda-m-0(NaCl) = 426 + 91 - 126 = 391 ohm-1 cm2 mol-1.
Note: The source paper gives 426 - 126 = 300, which appears to omit the CH3COONa contribution correctly only if applied differently. Using the standard Kohlrausch approach: Lambda-m-0(CH3COOH) = Lambda-m-0(CH3COONa) + Lambda-m-0(HCl) - Lambda-m-0(NaCl) = 91 + 426 - 126 = 391.
alpha = Lambda-m / Lambda-m-0 = 48.1 / 391 = 0.123. The paper reports 0.16 using 300 as the denominator. Be aware of which values your exam provides and apply the formula as given.
Isotonic solutions have equal osmotic pressure, so equal moles of solute per litre.
15 g urea (M = 60) in 1 L = 0.25 mol. For isotonic glucose (M = 180): 0.25 mol x 180 g/mol = 45 g glucose.
1 M KCl has higher osmotic pressure than 1 M urea because KCl dissociates into K+ and Cl- (two particles per formula unit), while urea does not dissociate.
Osmotic pressure is colligative: it depends only on particle count, not particle identity.
When RBCs are placed in 0.5% NaCl (hypotonic), water enters by osmosis, causing swelling and possible hemolysis.
Reverse osmosis requires applying external pressure > osmotic pressure. Used industrially for desalination and water purification.
Students mix up which electrode is cathode and which is anode when calculating Ecell. Remember: cathode = reduction, anode = oxidation. Ecell = Ecathode - Eanode.
Students assume osmotic pressure depends on the type of solute. It does not: it depends only on the number of particles. KCl produces twice as many particles as urea at the same molarity.
Students forget to account for dissociation when comparing osmotic pressures of electrolytes vs non-electrolytes.
⚠️ Nernst equation numericals appear in Section E (5 marks). Practise substituting into Ecell = E0cell - (0.0592/n) log Q. Watch the sign of log Q.
⚠️ Gibbs energy calculation: delta-G0 = -nFE0. A negative answer means spontaneous. This is a standard 3-mark problem.
⚠️ Isotonic solution problems: equal osmotic pressure means equal moles of solute. Convert mass to moles using molar mass.
⚠️ "Why is osmotic pressure a colligative property?" is a standard 1-mark question. Answer: it depends only on the number of solute particles, not their nature.
Q: A solution of 15 g urea (M = 60) per litre is isotonic with a glucose (M = 180) solution. What mass of glucose is present per litre?
A: Moles of urea = 15/60 = 0.25 mol. For isotonic solutions, moles of glucose = 0.25 mol. Mass of glucose = 0.25 x 180 = 45 g.
Q: Which has higher osmotic pressure: 1 M KCl or 1 M urea? Justify.
A: 1 M KCl. KCl dissociates into K+ and Cl- (2 particles per formula unit), so it has roughly double the particle concentration of 1 M urea (which does not dissociate). Osmotic pressure is proportional to particle count.
Q: Calculate delta-G0 for Au(s) + Ca2+(1M) --> Au3+(1M) + Ca(s), given E0(Au3+/Au) = +1.5 V and E0(Ca2+/Ca) = -2.87 V.
A: E0cell = 1.5 - (-2.87) = 4.37 V. n = 3. delta-G0 = -3 x 96500 x 4.37 = -1.26 x 10^6 J/mol. The reaction is spontaneous (negative delta-G0).
Electrochemistry connects directly to Chemical Kinetics (Ch. 3) through the Arrhenius equation and temperature dependence of reaction rates at electrodes. Solutions connect to Biomolecules (Ch. 14) through osmotic effects in biological systems (RBC hemolysis, cell turgidity).
Tags: electrochemistry, cell potential, Gibbs energy, Nernst equation, Faraday constant, fuel cell, molar conductivity, Kohlrausch law, degree of dissociation, osmotic pressure, colligative properties, isotonic, reverse osmosis, solutions, CBSE Class 12 Chemistry, Chapter 2, Chapter 4