Electrochemistry revision notes

Electrochemical Cell

A device that consists of two half-cells, each containing a metallic electrode dipped into an electrolyte. These half-cells are connected externally by a metallic wire (through a voltmeter and switch) and internally by a salt bridge. They are broadly classified into two types:

• Galvanic (Voltaic) Cell: An electrochemical cell that converts the chemical energy of a spontaneous redox reaction into electrical energy.
• Electrolytic Cell: A device that uses electrical energy to carry out non-spontaneous chemical reactions.

Daniell Cell (Example of a Galvanic Cell)

Converts chemical energy to electrical energy via: $Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq) + Cu(s)$. Standard cell potential is 1.1 V (when concentrations are 1 M).

Effect of External Opposing Potential ($E_{ext}$) on a Galvanic Cell

JEE Tip Highly tested concept regarding cell reversibility.

Cell Representation

Anode is on the left, cathode on the right. A double vertical line ($||$) represents the salt bridge. Example: $Cu(s)|Cu^{2+}(aq) || Ag^+(aq)|Ag(s)$.

Standard Hydrogen Electrode (SHE)

Assigned a zero potential at all temperatures. Consists of a platinum electrode coated with platinum black, dipped in 1 M $H^+$ solution, with pure $H_2$ gas bubbled at 1 bar.

• Reaction: $H^+(aq) + e^- \rightarrow \frac{1}{2}H_2(g)$.
• Used as a reference to find standard potentials of other half-cells.

Nernst Equation

Defines the relationship between electrode potential and concentration.

• For $M^{n+}(aq) + ne^- \rightarrow M(s)$: $E = E^\circ - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}$
• For a general reaction $aA + bB \rightleftharpoons cC + dD$: $E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• At 298 K, $\frac{2.303 RT}{F} = 0.059\ V$.
• JEE Tip The concentration of solid ($M$) and pure liquids is strictly taken as unity. Do not include them in the Nernst reaction quotient $Q$.

Equilibrium Constant from the Nernst Equation

At equilibrium, $E_{cell} = 0$ (The cell is dead) and reaction quotient $Q = K_c$.

• $E^\circ_{cell} = \frac{2.303 RT}{nF} \log K_c$

Gibbs Free Energy & Cell Potential

Electrical work done in one second is electrical potential multiplied by total charge. Maximum work requires reversible charge passage.

• $\Delta_r G = -nF E_{cell}$
• $\Delta_r G^\circ = -nF E^\circ_{cell}$

Electronic (Metallic) Conductance

• Definition: Electrical conductance through metals is due to the movement of electrons.
• Factors affecting it: It depends on (i) the nature and structure of the metal, (ii) the number of valence electrons per atom, and (iii) temperature.
• Relation with Temperature: Electronic conductance decreases with an increase in temperature.

Ionic (Electrolytic) Conductance

• Definition: Conductance of electricity by ions present in the solutions.
• Factors affecting it: It depends on (i) the nature of the electrolyte added, (ii) size of the ions produced and their solvation, (iii) the nature of the solvent and its viscosity, (iv) concentration of the electrolyte, and (v) temperature.
• Relation with Temperature: Ionic conductance increases with an increase in temperature.

Superconductors & Conducting Polymers

• Superconductors: Materials that by definition have zero resistivity or infinite conductivity. Earlier, only metals and their alloys at very low temperatures (0 to 15 K) were known to behave as superconductors, but nowadays a number of ceramic materials and mixed oxides are known to show superconductivity at temperatures as high as 150 K.
• Conducting Polymers: Organic polymers like polyacetylene (when exposed to iodine vapour), polyaniline, polypyrrole, and polythiophene exhibit metallic conductance. They are lightweight and possess the mechanical flexibility of plastics, making them suitable for electronic devices like bendable transistors and light-weight batteries (Nobel Prize in Chemistry, 2000).

Measurement of the Conductivity of Ionic Solutions

• The Problem with DC: Measuring resistance of an ionic solution faces two problems: (1) passing direct current (DC) changes the composition of the solution due to electrochemical reactions, and (2) a solution cannot be connected to a bridge like a solid wire.
• The Solution: The first difficulty is resolved by using an alternating current (AC) source of power (an oscillator operating in the audio frequency range 550 to 5000 cycles per second). The second problem is solved by using a specially designed vessel called a conductivity cell.

• Calculation: Once the cell constant is known, the unknown resistance $R_2$ is measured via a Wheatstone bridge ($R_2 = R_1 R_4 / R_3$), and the conductivity of the unknown solution is calculated as $\kappa = G^* / R$.

Variation of Conductivity and Molar Conductivity with Concentration

• Conductivity ($\kappa$): Always decreases with a decrease in concentration (upon dilution) for both weak and strong electrolytes. This is because the number of ions per unit volume that carry the current in a solution decreases on dilution.

• Limiting Molar Conductivity ($\Lambda_m^\circ$): When concentration approaches zero (infinite dilution), the molar conductivity is known as limiting molar conductivity.

Strong Electrolytes

• For strong electrolytes, $\Lambda_m$ increases slowly with dilution.
• Debye-Hückel-Onsager Equation: The variation can be represented by a straight-line equation: $\Lambda_m = \Lambda_m^\circ - A c^{1/2}$.
• The constant $A$ depends on the type of electrolyte (e.g., 1-1 for NaCl, 2-1 for CaCl2, 2-2 for MgSO4). All electrolytes of a particular type have the same value for 'A' at a given temperature and solvent.
• $\Lambda_m^\circ$ can be obtained easily by extrapolating the straight line graph to the y-axis (where $c = 0$).

Weak Electrolytes

• Weak electrolytes (e.g., acetic acid) have a lower degree of dissociation at higher concentrations.
• Steep Increase on Dilution: $\Lambda_m$ increases steeply on dilution, especially near lower concentrations, because the degree of dissociation ($\alpha$) increases, generating more ions in the total volume containing 1 mole of the electrolyte.
• Extrapolation Anomaly: Because the curve becomes very steep near zero concentration, $\Lambda_m^\circ$ cannot be obtained by extrapolating the graph to the y-axis. Instead, Kohlrausch's law is used to calculate it.

Kohlrausch Law of Independent Migration of Ions

The limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte.

• Formula: $\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$ (where $\nu_+$ and $\nu_-$ are the number of cations and anions per formula unit, and $\lambda_+^\circ$ and $\lambda_-^\circ$ are their respective limiting molar conductivities).
• Application: It is primarily used to calculate the limiting molar conductivity ($\Lambda_m^\circ$) for weak electrolytes using the known $\lambda^\circ$ values of individual ions or strong electrolytes.

Products depend on the nature of the material, type of electrodes (inert like Pt/Au vs reactive), and standard electrode potentials.

Rule of Preference

• Cathode: Species with a higher (more positive) standard reduction potential gets reduced preferentially.
• Anode: Species with a lower standard reduction potential gets oxidized preferentially.

Aqueous NaCl Electrolysis

• Cathode: $H_2O$ is reduced to $H_2(g)$ instead of $Na^+$ reducing to $Na(s)$ because $E^\circ(H_2O/H_2) > E^\circ(Na^+/Na)$.
• Anode: $Cl^-$ is oxidized to $Cl_2(g)$ instead of $H_2O$ oxidizing to $O_2(g)$ due to overpotential.
• Net cell product: $H_2$, $Cl_2$, and $NaOH(aq)$ remaining in solution.

Sulfuric Acid Electrolysis ($H_2SO_4$)

• Dilute $H_2SO_4$: Water is oxidized at the anode: $2H_2O(l) \rightarrow O_2(g) + 4H^+(aq) + 4e^-$.
• Concentrated $H_2SO_4$: Sulfate is oxidized at the anode: $2SO_4^{2-}(aq) \rightarrow S_2O_8^{2-}(aq) + 2e^-$ (forms peroxodisulphate).

Primary Batteries (Non-rechargeable)

Secondary Batteries (Rechargeable)

Fuel Cells & The Hydrogen Economy

Galvanic cells directly converting combustion energy of fuels ($H_2$, $CH_4$, $CH_3OH$) into electricity. The "Hydrogen Economy" is a vision where hydrogen is produced via solar water splitting and consumed in fuel cells, producing only water and zero pollution.

An electrochemical phenomenon where metal is oxidized to oxides/salts.

Rusting of Iron

• Anode spot: $2Fe \rightarrow 2Fe^{2+} + 4e^-$ ($E^\circ = -0.44\ V$)
• Cathode spot: Electrons reduce $O_2$ in presence of $H^+$: $O_2(g) + 4H^+(aq) + 4e^- \rightarrow 2H_2O(l)$ ($E^\circ = 1.23\ V$)
• Overall: $2Fe + O_2 + 4H^+ \rightarrow 2Fe^{2+} + 2H_2O$ ($E^\circ_{cell} = 1.67\ V$)
• $Fe^{2+}$ further oxidizes to form rust: $Fe_2O_3 \cdot xH_2O$.

Prevention

Paint, bisphenol, galvanizing (Sn, Zn), or using a sacrificial electrode (Mg, Zn) which corrodes instead of the target object.

• Cell Potential: $E_{cell} = E_{right} - E_{left} = E_{cathode} - E_{anode}$
• Nernst Eq at 298 K: $E_{cell} = E^\circ_{cell} - \frac{0.059}{n} \log \frac{[Products]}{[Reactants]}$
• Standard Gibbs Free Energy: $\Delta_r G^\circ = -nF E^\circ_{cell} = -RT \ln K_c$
• Resistance: $R = \rho \frac{l}{A}$
• Conductivity: $\kappa = \frac{1}{\rho} = \frac{1}{R} \times \frac{l}{A} = \frac{G^*}{R}$
• Molar Conductivity (crucial conversion format): $\Lambda_m \ (S\ cm^2\ mol^{-1}) = \frac{\kappa\ (S\ cm^{-1}) \times 1000}{Molarity\ (mol\ L^{-1})}$
• Kohlrausch's Law: $\Lambda_m^\circ (A_xB_y) = x\lambda_m^\circ (A^{y+}) + y\lambda_m^\circ (B^{x-})$
• Degree of Dissociation: $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ}$
• Charge/Faraday: $Q = It$. 1 Faraday ($F$) $= 96487\ C\ mol^{-1}$ (Approx $96500\ C$).

• Nernst Equation with pH/Ksp: Frequently, the concentration of $H^+$ is not given directly but via pH. ($pH = -\log[H^+]$).
• Calculations using Kohlrausch Law: Finding $\Lambda_m^\circ$ for weak acids (like $\Lambda_m^\circ(CH_3COOH)$) using a combination of strong electrolytes ($\Lambda_m^\circ(CH_3COONa) + \Lambda_m^\circ(HCl) - \Lambda_m^\circ(NaCl)$).
• Faraday's Laws Numericals: Determining the time required to deposit a certain mass, or mass deposited given current and time.
• Predicting Products of Electrolysis: MCQ traps differentiating between molten salts (only one possible reduction/oxidation) and aqueous solutions (competition with water).
• Conductivity Cell Constant: Back-calculating the cell constant $G^*$ using a reference $KCl$ solution, then applying it to an unknown solution.