Revision Notes for CBSE Class 12 Chemistry Chapter 3: Electrochemistry

Essential Glossary of Terms

Electrochemical Cell

A device that converts the chemical energy released during a spontaneous redox reaction into electrical energy.

Electrolytic Cell

A device that uses electrical energy from an external source to force a non-spontaneous chemical reaction to occur.

Standard Electrode Potential ($E^0$)

The potential difference developed between a metal electrode and its solution containing metal ions at unit concentration ($1\text{ M}$) at a temperature of $298\text{ K}$ and $1\text{ bar}$ pressure.

Conductivity (Specific Conductance, $\kappa$)

The reciprocal of resistivity, representing the conductance of a solution of $1\text{ cm}$ length and $1\text{ cm}^2$ area of cross-section. Measured in $\text{S cm}^{-1}$ or $\text{S m}^{-1}$.

Molar Conductivity ($\Lambda_m$)

The conducting power of all the ions produced by dissolving one mole of an electrolyte in a solution. Mathematically, $\Lambda_m = \frac{\kappa \times 1000}{M}$.

Limiting Molar Conductivity ($\Lambda_m^0$)

The molar conductivity of an electrolyte when the concentration of the solute approaches zero (infinite dilution).

Faraday's Constant ($F$)

The total electrical charge carried by one mole of electrons, approximately equal to $96487\text{ C mol}^{-1}$ (commonly rounded to $96500\text{ C}$).

Understanding the Nernst Equation & Cell Thermodynamics

The potential of an electrochemical cell is fundamentally dependent on the concentration of the reacting ions and the system's temperature. The Nernst Equation mathematically represents this relationship. For a general reduction reaction occurring at an electrode: $M^{n+}(aq) + ne^- \rightarrow M(s)$, the electrode potential is given by:

$E_{(M^{n+}/M)} = E^0_{(M^{n+}/M)} - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}$

When we generalize this for a complete cell reaction at standard temperature ($298\text{ K}$), converting the natural logarithm to base 10, the equation simplifies to:

$E_{\text{cell}} = E^0_{\text{cell}} - \frac{0.0591}{n} \log \frac{[\text{Products}]}{[\text{Reactants}]}$

Gibbs Free Energy and Cell Potential:
Thermodynamically, the maximum electrical work done by an electrochemical cell is equal to the decrease in Gibbs Free Energy ($\Delta_r G$). The mathematical relationship is expressed as:

$\Delta_r G = -nFE_{\text{cell}}$

Under standard state conditions, this becomes:

$\Delta_r G^0 = -nFE^0_{\text{cell}}$

If the cell reaction reaches chemical equilibrium, the cell potential ($E_{\text{cell}}$) drops to zero, and the reaction quotient ($Q$) becomes equal to the equilibrium constant ($K_c$). Rearranging the Nernst equation at $298\text{ K}$ yields: $E^0_{\text{cell}} = \frac{0.0591}{n} \log K_c$.

Galvanic Cells vs. Electrolytic Cells

Step-by-Step Molar Conductivity & Kohlrausch's Law Calculations

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Step-by-Step Solved Numericals

• {"title":"Example 1: Calculating Standard Gibbs Energy and Equilibrium Constant","bodyMarkdown":"Question: Calculate the standard Gibbs energy ($\\Delta G^0$) and equilibrium constant ($K_c$) for the cell reaction: $\\text{Zn}(s) + \\text{Cu}^{2+}(aq) \\rightarrow \\text{Zn}^{2+}(aq) + \\text{Cu}(s)$ given $E^0_{\\text{cell}} = 1.10\\text{ V}$.\n\nSolution:\n1. Identify the number of transferred electrons ($n$) = $2$.\n2. Compute $\\Delta G^0$ using $\\Delta G^0 = -nFE^0_{\\text{cell}}$:\n $\\Delta G^0 = -2 \\times 96500 \\times 1.10 = -212,300\\text{ J mol}^{-1} = -212.3\\text{ kJ mol}^{-1}$\n3. Calculate $K_c$ using $\\log K_c = \\frac{n E^0_{\\text{cell}}}{0.0591}$:\n $\\log K_c = \\frac{2 \\times 1.10}{0.0591} = 37.22 \\implies K_c = 1.66 \\times 10^{37}$"}
• {"title":"Example 2: Applying Faraday's Laws of Electrolysis","bodyMarkdown":"Question: A solution of $\\text{CuSO}_4$ is electrolyzed for 10 minutes with a current of 1.5 amperes. What is the mass of copper deposited at the cathode? (Atomic mass of $\\text{Cu} = 63.5\\text{ g mol}^{-1}$)\n\nSolution:\n1. Convert time to seconds: $t = 10 \\times 60 = 600\\text{ s}$.\n2. Calculate total charge passed ($Q = I \\times t$):\n $Q = 1.5\\text{ A} \\times 600\\text{ s} = 900\\text{ C}$\n3. The cathode reaction is: $\\text{Cu}^{2+} + 2e^- \\rightarrow \\text{Cu}(s)$.\n This shows $2$ moles of electrons ($2 \\times 96500\\text{ C}$) deposit $1$ mole of $\\text{Cu}$ ($63.5\\text{ g}$).\n4. Use proportion to find mass ($w$):\n $w = \\frac{63.5}{2 \\times 96500} \\times 900 = 0.296\\text{ g}$"}

Must-Remember Revision Points

• Oxidation always occurs at the anode, and reduction always occurs at the cathode, regardless of whether it is a Galvanic or Electrolytic cell.
• Specific conductivity ($\kappa$) always decreases with a decrease in concentration (dilution) for both strong and weak electrolytes because the number of current-carrying ions per unit volume decreases.
• Molar conductivity ($\Lambda_m$) increases with dilution. Strong electrolytes experience a gradual, linear increase due to decreased inter-ionic attractions (described by Debye-Hückel-Onsager equation).
• Weak electrolytes display a steep increase in molar conductivity ($\Lambda_m$) at high dilution due to a significant increase in the degree of dissociation ($\alpha$).
• In the electrochemical series, elements with lower standard reduction potentials act as stronger reducing agents, while those with higher standard reduction potentials act as stronger oxidizing agents.
• Primary cells (like Dry Cell, Mercury Cell) cannot be recharged, whereas Secondary cells (like Lead Storage Battery, Ni-Cd Cell) can be recharged by reversing the current flow.
• Corrosion of iron is an electrochemical phenomenon where rust is formed at anodic spots on the metal surface: $\text{Fe} \rightarrow \text{Fe}^{2+} + 2e^-$, combined with cathodic reduction of oxygen in an acidic medium.
• In a dry cell, the manganese dioxide ($MnO_2$) acts as a depolarizer to oxidize hydrogen gas into water, preventing gas buildup.

CBSE Board Exam Traps & Marking Guidelines

• Unit Conversions: The biggest trap in Electrochemistry numericals is units! If conductivity ($\kappa$) is given in $\text{S m}^{-1}$ instead of $\text{S cm}^{-1}$, you must use the formula $\Lambda_m = \frac{\kappa}{1000 \times M}$ where $M$ is in $\text{mol L}^{-1}$. Always verify whether you are working in CGS or SI units before starting calculations.
• Writing Cell Representations: Always write physical states such as $(s)$, $(aq)$, and $(g)$ alongside the concentration of electrolytes in brackets. Follow the standard LOAN acronym (Left, Oxidation, Anode, Negative) to construct cell diagrams.
• Showing Formula Steps: CBSE marking schemes allocate step-wise marks. Write down the blank formula (e.g., $E_{\text{cell}} = E^0_{\text{cell}} - \frac{0.0591}{n} \log Q$) before substituting numerical values to secure partial marks even if you make a calculation error.

Practice Questions with Solutions

• Why does conductivity of a solution decrease with dilution? Conductivity is defined as the conductance of ions present in a unit volume of solution. Dilution increases the overall volume of the solution, which reduces the number of current-carrying ions per unit volume, leading to a decrease in conductivity.
• Can we store copper sulfate solution in an iron vessel? Why? No. The standard reduction potential of iron is lower than that of copper ($E^0_{\text{Fe}^{2+}/\text{Fe}} = -0.44\text{ V}$, $E^0_{\text{Cu}^{2+}/\text{Cu}} = +0.34\text{ V}$). This makes iron more reactive than copper, meaning it will displace copper from the solution, corroding the iron vessel.
• State Kohlrausch's law of independent migration of ions. Kohlrausch's Law states that at infinite dilution, where dissociation of the electrolyte is complete, each ion makes a definite individual contribution towards the limiting molar conductivity of the electrolyte, regardless of the nature of the other ion present.
• What is the role of a salt bridge in a Galvanic cell? A salt bridge completes the electrical circuit by allowing migration of ions between half-cells, maintaining electrical neutrality in both compartments and preventing the accumulation of charges.

Frequently Asked Questions