Chapter 2: Electrochemistry
Key Topics: Electrolytic Conductance, Kohlrausch's Law, Galvanic Cells, Nernst Equation, Gibbs Free Energy, and Faraday's Laws of Electrolysis.
1. Electrochemical Cells
Electrochemistry deals with the interconversion of chemical energy and electrical energy.
- Galvanic (Voltaic) Cell: Converts chemical energy of a spontaneous redox reaction into electrical energy (e.g., Daniell Cell).
- Electrolytic Cell: Uses electrical energy to drive a non-spontaneous chemical reaction.
Overall Cell Reaction (Daniell Cell):
$$\text{Zn(s)} + \text{Cu}^{2+}\text{(aq)} \rightarrow \text{Zn}^{2+}\text{(aq)} + \text{Cu(s)}$$
2. Resistance, Conductance & Conductivity
Electrical Resistance ($R$) & Resistivity ($\rho$):
$$R = \rho \frac{l}{A}$$
Conductance ($G$) & Conductivity ($\kappa$):
$$G = \frac{1}{R}$$
$$\kappa = G \times \left( \frac{l}{A} \right)$$
Where $\frac{l}{A}$ is the Cell Constant ($G^*$).
Molar Conductivity ($\Lambda_m$):
Conductivity per unit molar concentration of electrolyte:
$$\Lambda_m = \frac{\kappa \times 1000}{C}$$
Where $\kappa$ is in $\text{S cm}^{-1}$ and $C$ (Molarity) is in $\text{mol L}^{-1}$.
3. Variation of Conductivity & Kohlrausch's Law
Debye-Hückel-Onsager Equation (For Strong Electrolytes):
$$\Lambda_m = \Lambda_m^\circ - A\sqrt{C}$$
Kohlrausch's 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:
$$\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$$
4. Nernst Equation & Cell EMF
Electrode Potential Equation:
For a general reduction reaction $M^{n+}\text{(aq)} + n e^- \rightarrow M\text{(s)}$:
$$E_{(M^{n+}/M)} = E^\circ_{(M^{n+}/M)} - \frac{RT}{nF} \ln \frac{1}{[M^{n+}]}$$
Cell EMF at Standard Temperature ($298\text{ K}$):
For a reaction $aA + bB \rightarrow cC + dD$:
$$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{0.0591}{n} \log_{10} \frac{[C]^c [D]^d}{[A]^a [B]^b}$$
Standard Cell Potential Calculation:
$$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$
5. Gibbs Energy & Equilibrium Constant
Standard Gibbs Free Energy ($\Delta_r G^\circ$):
$$\Delta_r G^\circ = -n F E^\circ_{\text{cell}}$$
Relation between $\Delta_r G^\circ$ and Equilibrium Constant ($K_c$):
$$\Delta_r G^\circ = -2.303 R T \log_{10} K_c$$
$$E^\circ_{\text{cell}} = \frac{0.0591}{n} \log_{10} K_c \quad (\text{at } 298\text{ K})$$
6. Faraday's Laws of Electrolysis
Faraday's First Law:
The mass of substance deposited ($m$) is directly proportional to the quantity of electricity passed ($Q$):
$$m = Z \cdot Q = Z \cdot I \cdot t$$
Where $Z$ is the Electrochemical Equivalent, $I$ is current in Amperes, and $t$ is time in seconds.
Faraday's Second Law:
When the same quantity of electricity is passed through different electrolytes, the masses deposited are proportional to their chemical equivalent weights:
$$\frac{w_1}{w_2} = \frac{E_1}{E_2}$$