JEE Chemistry Electrochemistry Notes Set 02

Conductors and Electrolytes

A conductor lets electric current pass. Metals carry current by moving electrons and nothing in them changes chemically. Electrolytes (aqueous solutions or melts of acids, bases and salts) carry current by moving ions, and the passage of current causes chemical change at the electrodes. A strong electrolyte is fully ionised at every concentration (strong acids, strong bases, most salts). A weak electrolyte ionises only partly (acetic acid, HCN, ammonia, amines).

Resistance, Conductance and Conductivity

1. Resistance \( R = V/I \) (ohm). Conductance \( G = 1/R \) (siemens, S, or mho, \( \Omega^{-1} \)).
2. For a block of length \( \ell \) and cross-section \( A \): \( R = \rho \ell / A \), where \( \rho \) is the resistivity (ohm cm).
3. Conductivity (specific conductance) \( \kappa = 1/\rho \), in \( \Omega^{-1} \text{cm}^{-1} \). It is the conductance of 1 cm cube of the solution.
4. Cell constant \( G^* = \ell / A \) (cm\( ^{-1} \)). Then \( \kappa = G \times G^* = G^*/R \). The cell constant is found by filling the cell with a KCl solution of known conductivity.

Molar and Equivalent Conductivity

Molar conductivity \( \Lambda_m \) is the conductivity of all the ions produced by one mole of electrolyte in the volume V that contains that mole. Equivalent conductivity \( \Lambda_{eq} \) is the same idea for one gram equivalent.

\[ \Lambda_m = \kappa V = \frac{1000\,\kappa}{M} \qquad \Lambda_{eq} = \frac{1000\,\kappa}{N} \qquad \Lambda_{eq} = \frac{\Lambda_m}{\text{valency factor}} \]

Use \( \kappa \) in \( \Omega^{-1} \text{cm}^{-1} \) and concentration in mol/L in these formulas. If SI units are used (\( \kappa \) in S m\( ^{-1} \)), then \( \Lambda_m = \kappa / C \) with C in mol m\( ^{-3} \), and the answer is in S m\( ^2 \) mol\( ^{-1} \). Remember 1 S m\( ^2 \) mol\( ^{-1} \) = 10\( ^4 \) S cm\( ^2 \) mol\( ^{-1} \).

Worked Examples

1. A 1 N solution has resistance 50 ohm between electrodes 2.1 cm apart, each of area 4.2 cm\( ^2 \). Cell constant = 2.1/4.2 = 0.5 cm\( ^{-1} \), so \( \kappa = 0.5/50 = 0.01 \). Then \( \Lambda_{eq} = 1000 \times 0.01/1 = 10 \) ohm\( ^{-1} \) cm\( ^2 \) eq\( ^{-1} \).
2. Compare 0.08 M with \( \kappa = 2 \times 10^{-2} \) and 0.1 M with resistivity 50 ohm cm. First: \( \Lambda_m = 1000 \times 0.02/0.08 = 250 \). Second: \( \kappa = 1/50 = 0.02 \), so \( \Lambda_m = 1000 \times 0.02/0.1 = 200 \). The 0.08 M solution has the larger molar conductivity.
3. Equal volumes of 0.015 M acetic acid and 0.015 M NaOH are mixed, giving sodium acetate at 0.0075 M. If its conductivity is \( 6.3 \times 10^{-4} \) S cm\( ^{-1} \), then \( \Lambda_m = 6.3 \times 10^{-4} \times 1000/0.0075 = 84 \) S cm\( ^2 \) mol\( ^{-1} \).

Factors Affecting Conductance

1. Inter-ionic attraction: stronger attraction between ions lowers conductance.
2. Polarity of solvent: a solvent of high dielectric constant ionises the solute better and gives higher conductance.
3. Viscosity of the medium: higher viscosity lowers conductance.
4. Temperature: conductance of electrolytes rises with temperature.
5. Hydration: a larger hydrated ion moves more slowly, so conductance is lower.
6. Dilution: conductance G increases on dilution, but conductivity \( \kappa \) falls (fewer ions per cm\( ^3 \)). Both \( \Lambda_m \) and \( \Lambda_{eq} \) increase. In a strong electrolyte the cause is reduced inter-ionic attraction (greater ion mobility). In a weak electrolyte the cause is greater degree of ionisation.

Variation with Concentration

For strong electrolytes the Debye-Huckel-Onsager equation holds: \( \Lambda_m = \Lambda_m^\circ - b\sqrt{C} \). A plot of \( \Lambda_m \) against \( \sqrt{C} \) is a straight line, and its intercept gives the limiting value \( \Lambda_m^\circ \). For weak electrolytes the curve rises very steeply at low concentration and cannot be extrapolated, so \( \Lambda^\circ \) is found by Kohlrausch's law.