Electrolytic Solutions

Ohm's law states that the resistance R (in ohms, Ω) of a conductor equals the voltage V divided by the current I: R = V/I. For a uniform conductor of cross-sectional area A and length l, the resistance is also R = ρ·l/A, where ρ is the resistivity (Ω·m). In practice, the resistance of an electrolytic solution is measured with an alternating-current (AC) Wheatstone bridge to avoid electrolysis and polarisation effects at the electrodes.

Conductance G is the reciprocal of resistance: G = 1/R. Its SI unit is the siemens (S), where 1 S = 1 Ω⁻¹. A large conductance means the solution allows current to pass easily. Because conductance depends on cell geometry (how far apart the electrodes are and how large they are), it is not an intrinsic property of the electrolyte itself.

To remove the geometry dependence, we define conductivity κ (kappa) as κ = G · (l/A). Here l/A is called the cell constant (G*) of the conductivity cell and has units m⁻¹. Conductivity has units S·m⁻¹ (or, commonly in chemistry, S·cm⁻¹). At a given temperature and concentration, κ is a fixed property of the solution. For strong electrolytes, κ increases with concentration because there are more ions per unit volume, but it eventually levels off due to interionic attractions.

Molar conductivity Λm is defined as Λm = κ/c, where c is the molar concentration in mol·m⁻³ (note: if c is in mol·L⁻¹, multiply by 1000 to convert). Its unit is S·m²·mol⁻¹. Λm represents the conductivity of a solution containing exactly one mole of electrolyte, stretched to fill the space between two electrodes. For strong electrolytes (fully dissociated, e.g., KCl, HCl), Λm increases only slightly with dilution because the fraction of dissociated ions is already 1 but interionic forces weaken. For weak electrolytes (e.g., acetic acid, CH₃COOH), Λm increases dramatically upon dilution because dilution drives the dissociation equilibrium towards more ions.

Friedrich Kohlrausch discovered empirically that for strong electrolytes: Λm = Λ°m − K√c, where Λ°m is the limiting molar conductivity (at infinite dilution) and K is a constant that depends on the electrolyte type. At infinite dilution, ions do not interact with each other, and Kohlrausch's Law of Independent Migration of Ions states that Λ°m = ν₊λ°₊ + ν₋λ°₋, where ν₊ and ν₋ are the stoichiometric numbers of cations and anions, and λ°₊ and λ°₋ are their individual limiting molar ionic conductivities.

For a weak electrolyte, the degree of dissociation α can be estimated as α = Λm / Λ°m. Since Λ°m for a weak electrolyte cannot be measured directly (it never fully dissociates), it is calculated from tabulated ionic values using Kohlrausch's law of independent migration. Once α is known, the dissociation constant Ka can be found: Ka = cα² / (1−α).

• \Lambda_m — Molar Conductivity (S\,m^2\,mol^{-1}): The conductivity of a solution containing one mole of electrolyte, normalised per mole.
• \kappa — Conductivity (Specific Conductance) (S\,m^{-1}): The inherent ability of the solution to conduct electricity, independent of cell geometry.
• c — Molar Concentration (mol\,m^{-3}): Amount of electrolyte dissolved per cubic metre of solution (1 mol/L = 1000 mol/m³).

Problem. A 0.020 mol/L solution of potassium chloride (KCl) has a measured conductance of 2.55 × 10⁻³ S in a cell whose cell constant (l/A) is 50.0 m⁻¹. Calculate (a) the conductivity κ of the solution and (b) the molar conductivity Λm.

Answer. κ = 0.1275 S·m⁻¹; Λm = 6.375 × 10⁻³ S·m²·mol⁻¹ (= 63.75 S·cm²·mol⁻¹)

• Strong and Weak Electrolytes — Molar conductivity behaviour (Kohlrausch plot shape) directly reflects whether an electrolyte is strong (fully dissociated) or weak (partially dissociated); understanding dissociation is prerequisite to interpreting conductance data.
• Electrochemical Cells — Conductivity of electrolyte solutions determines internal resistance and efficiency of galvanic and electrolytic cells, directly linking conductance theory to practical cell design.
• Degree of Dissociation and Ka — The ratio α = Λm/Λ°m gives the degree of dissociation of a weak electrolyte, which feeds directly into the acid dissociation constant Ka calculation.
• Ohm's Law and Electrical Circuits — Resistance, voltage, and current relationships from Ohm's law are the starting point for defining conductance G = 1/R in electrolytic solutions.