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
         A = area of electrodes

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 (Lm) or equivalent conductivity (L)

Lm = k/c and L = k/n

where c = molar concentration (in units of mol/cm3) and
          n = equivalent concentration (in units of equiv./cm3)

Kohlrausch's Law relates the variation of molar conductivity with concentration for strong electrolytes.

Lm = Lom - K c1/2

where K = is a constant that is dependent on solvent and electrolyte
           Lom = the limiting molar conductivity
           c = molar concentration

Limiting molar conductivity (Lom) and Kohlrausch's constant (K) can be obtained from a fit of molar conductivity (Lm) versus the square root of concentration (c1/2)

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
n's are the number of ions

For weak electrolytes conductivity data can be used to calculate the fraction dissociated (a)

a = Lm/Lom

so for a 1:1 weak electrolyte

Kd = c a2 /[(1 - a) co] = c(Lm/Lom)2/[(1 - Lm/Lom) co]

linearizing

1/Lm = 1/Lom + (Lm c)/[Kd (Lom)2]

so fit 1/Lm vs (Lm * c)

your intercept, b = 1/Lom or Lom = 1/b

and you slope, m = 1/[Kd (Lom)2] or Kd = b2/m