JEE Chemistry Electrochemistry Notes Set 03

Kohlrausch's Law and Its Uses

At infinite dilution each ion migrates independently and contributes a fixed amount to the conductivity, whatever the other ion is. For an electrolyte \( A_xB_y \): \( \Lambda_m^\circ = x\,\lambda^\circ_{+} + y\,\lambda^\circ_{-} \), and \( \Lambda_{eq}^\circ = \lambda^\circ_{+} + \lambda^\circ_{-} \) when the ionic values are per equivalent.

1. Limiting conductivity of a weak electrolyte by combination, for example \( \Lambda^\circ(\text{CH}_3\text{COOH}) = \Lambda^\circ(\text{CH}_3\text{COONa}) + \Lambda^\circ(\text{HCl}) - \Lambda^\circ(\text{NaCl}) \).
2. Degree of dissociation \( \alpha = \Lambda / \Lambda^\circ \) (molar over molar or equivalent over equivalent).
3. Dissociation constant of a weak electrolyte \( K_a = C\alpha^2/(1-\alpha) \), which is about \( C\alpha^2 \) when \( \alpha \) is below 5 percent.
4. Solubility of a sparingly soluble salt: its saturated solution is almost infinitely dilute, so \( S = 1000\,\kappa / \Lambda^\circ_m \) (after subtracting the conductivity of water). For a salt giving \( n_+ \) and \( n_- \) ions, \( K_{sp} \) follows from S. For Ag\( _3 \)PO\( _4 \), \( K_{sp} = 27S^4 \).

Ionic conductivity is proportional to ionic mobility, \( \lambda = F u \). The transport number of an ion is the fraction of the total current it carries: \( t_+ = u_+/(u_+ + u_-) \), and \( t_+ + t_- = 1 \). When \( u_+ = u_- \), each transport number is 0.5.

Galvanic Cell

A galvanic (voltaic) cell turns the chemical energy of a spontaneous redox reaction into electrical energy. Two half cells (a metal in a solution of its ions) are joined by a wire and by a salt bridge. Oxidation occurs at the anode (negative pole) and reduction at the cathode (positive pole). Electrons flow from anode to cathode in the wire, while current is taken to flow the opposite way.

1. Salt bridge: an inverted U-tube with an inert electrolyte (KCl, KNO\( _3 \), NH\( _4 \)NO\( _3 \)) set in agar or gelatin. The cation and anion should move at nearly the same speed. KCl is avoided when Ag\( ^+ \), Pb\( ^{2+} \), Hg\( _2^{2+} \) or Tl\( ^+ \) are present because they would precipitate as chlorides.
2. Functions of the bridge: it completes the circuit, keeps each half cell electrically neutral, and removes the liquid junction potential. If it is taken out, the voltage drops to zero.
3. Cell notation: anode on the left, cathode on the right, a single line for a phase boundary, a double line for the salt bridge, for example Zn(s) | ZnSO\( _4 \)(aq) || CuSO\( _4 \)(aq) | Cu(s). Gas pressures and concentrations are written in brackets.

Electrode Potential and Reference Electrodes

The electrode potential is the potential difference between a metal and the solution of its ions. Standard electrode potential refers to 1 M ions, 1 bar for gases and 298 K. Oxidation potential and reduction potential of the same half cell have equal size and opposite sign. The higher the reduction potential, the greater the tendency to be reduced.

1. A single electrode potential cannot be measured, only differences. All values are given against the standard hydrogen electrode, SHE: Pt, H\( _2 \)(1 bar) | H\( ^+ \)(1 M), whose potential is taken as exactly zero. Platinum black adsorbs hydrogen and acts as the catalyst.
2. Secondary reference electrodes are easier to handle: the calomel electrode Hg-Hg\( _2 \)Cl\( _2 \) | KCl, and the silver-silver chloride electrode Ag-AgCl | KCl.

\[ E^\circ_{cell} = E^\circ_{red}(\text{cathode}) - E^\circ_{red}(\text{anode}) = \text{SRP(cathode)} + \text{SOP(anode)} \]

Electrode potential is an intensive property, so it is not multiplied when a half reaction is multiplied. Free energy is extensive: \( \Delta G^\circ = -nFE^\circ \). To combine half reactions with different numbers of electrons, add the \( \Delta G^\circ \) values. For example, from \( E^\circ(\text{Au}^+/\text{Au}) = 1.69 \) V and \( E^\circ(\text{Au}^{3+}/\text{Au}) = 1.40 \) V, \( -2FE^\circ = -3F(1.40) + F(1.69) \), giving \( E^\circ(\text{Au}^{3+}/\text{Au}^+) = 1.255 \) V.

Electrochemical Series

1. Oxidising power rises with E\( ^\circ_{red} \), and reducing power rises as E\( ^\circ_{red} \) falls.
2. A metal displaces from solution any metal that lies below it in the series, and the more reactive non-metal displaces the less reactive one (Cl\( _2 \) displaces Br\( ^- \) and I\( ^- \)).
3. A metal above hydrogen liberates H\( _2 \) from dilute acids (Zn does, Cu does not).