Chem 4300

Conductivity

Conductance G = 1/R, expressed in W^{1}(mho) or S (siemens) where 1 W^{1} = 1 S Conductance is a extensive property, the intensive version is conductivity, k k = G * l / A where l = distance between electrodes and Experimentally we will just convert l/A to a cell constant so k = k G = k / R k is just determined by the measurement of the conductance or resistance of a solution for which the conductivity is known, generally a KCl solution. The units of specific conductivity (k) are generally in W^{1} cm^{1} the units of the constant k are in cm^{1}. Since we are working in a solution of some concentration we make one further conversion to either molar conductivity (L_{m}) or equivalent conductivity (L) L_{m} = k/c and L = k/n where c = molar concentration (in units of mol/cm^{3}) and Kohlrausch's Law relates the variation of molar conductivity with concentration for strong electrolytes. L_{m} = L^{o}_{m}  K c^{1/2} where K = is a constant that is dependent
on solvent and electrolyte Limiting molar conductivity (L^{o}_{m}) and Kohlrausch's constant (K) can be obtained from a fit of molar conductivity (L_{m}) versus the square root of concentration (c^{1/2}) Kohlrausch also noted that the limiting conductivity of a salt in solution was related to the limiting conductivity of the ions according to the following equation Lom = n_{+} l_{+} + n_{} l_{} where l's are the conductivity of the ions
and For weak electrolytes conductivity data can be used to calculate the fraction dissociated (a) a = L_{m}/L^{o}_{m} so for a 1:1 weak electrolyte K_{d} = c a^{2} /[(1  a) c^{o}] = c(L_{m}/L^{o}_{m})^{2}/[(1  L_{m}/L^{o}_{m}) c^{o}] linearizing 1/L_{m} = 1/L^{o}_{m} + (L_{m} c)/[K_{d} (L^{o}_{m})^{2}] so fit 1/L_{m} vs (L_{m} * c) your intercept, b = 1/L^{o}_{m} or L^{o}_{m} = 1/b and you slope, m = 1/[K_{d} (L^{o}^{m})^{2}]
or K_{d} = b^{2}/m
