Equivalent Conductivity:
It is defined as the conductivity of all ions produced by 1 gram equivalent of electrolyte dissolved in a given solution. It is denoted by Λeq Suppose 1 cm³ of a solution of an electrolyte is placed between two electrodes kept 1 cm of the solution.
Thus, specific conductance (K)
K = conductance x l/a
= conductance x 1/1 = conductance
Similarly, if 1g equivalent electrolyte dissolved in 1 cm of solution, then conductance is equivalent conductance. If 1 cm3 of the above solution containing 1g equivalent of the electrolyte is diluted to 100 cm³, then there are 100 cm3 of the material and thus, the equivalent conductance will be 100 times the specific conductance.
Equivalent conductance,
Λeq 100 x specific conductance
On successive dilution to 100 cm³
Λeq = 1000 x specific conductance
In general Λeq = k x volume of the solution containing 1g equivalent of electrolyte. If concentration of the solution is Ceq gram equivalent per litre (i.e. normality), then the volume containing 1gm equivalent of the electrolyte will be 1/Ceq liters of 10000/Ceq cm³.
Λeq = k X V
Λeq = 1000 x K/Ceq
Λeq = 1000 x K/Normality
k(specific conductance) is in scm inverse and V is in equivalent-¹ cm³, hence, Λeq is practically written in the unit of Scm² equivalent-¹.
Molar Conductivity:
If the concentration is expressed in mol L-¹ i.e. Cm the volume (in cm³) containing 1 mole of the electrolyte is 1000 cm³, then the term molar conductance or molar conductivity is used. Therefore, molar conductivity is defined as the conductivity of all ions produced by one mole of electrolyte in a given solution.
Λm = 1000 K/Cm
Λm is expressed in the unit of Scm² mol-¹
Relation between Equivalent and Molar Conductivity-
The equivalent and molar conductivity are related by
Λm = Z.Λeq
z+ and z- are the absolute values of the valencies on the ions formed.
Species z
NaCl 1
CaCl₂ 2
BaSO4 2
AICI3 3
Na₂CO3 2
Variation of Conductivity with Concentration:-
Conductivity (or specific conductivity, k) of an electrolyte changes with the concentration of the electrolyte. For weak electrolytes and strong electrolytes, the conductivity always decreases as the concentration decreases, because the number of ions per unit volume carrying current in the solution decreases with dilution.
On the other hand for both weak and strong electrolytes, the electrolytic conductance as well as the equivalent conductivity (Λeq) and molar conductivity (Λm) increase with dilution (or decrease in concentration). This is due to the total vol. V of the solution containing one mole of electrolyte also increases.
Λeq = k X V
Λm = k XV
It has been located that lower in k on dilution of an answer is extra than compensated via way of means of growth in its volume.
Note :- Conductivity of strong electrolytes is higher in comparison to weak electrolyte because strong electrolytes dissociate completely and produce more ions in their solutions resulting to higher conductivity.
Variation of Molar Conductivity with Dilution (or Concentration)
The variation of molar conductivity with dilution (or concentration) is different for strong and weak electrolytes.
For Strong Electrolyte
In the lower concentration range, the molar conductivity of strong electrolytes is found to vary with concentration by the following equation called Debye-Huckel Onsager equation.
Λm = Λm - AC¹/2
Where A is a constant depending upon the type of electrolyte, the nature of the solvent and temperature.
Λm is the limiting value of the molar conductivity at
infinite dilution i.e. when C → 0
If a graph of Λm is plotted against √C, a straight line with an intercept equal to A., and slope equal to A is obtained at lower concentration. However, this graph is not linear for higher concentration.
| Variance of Λm with √C of strong electrolyte |
From the above curve, it is clearly shown that these is only a slight increase in the conductance with dilution (or decrease in concentration). This is due to the complete dissociation of a strong electrolyte in solution and so, the number of ions remains almost constant. However, at higher concentration, there will be a decrease in conductance of a solution.
This decrease is not due to a change in the number of ions with concentration, but due to change in the inter ionic attractions. At high concentrations, there are greater number of ions per unit volume which increases attraction between cation (K) and anion (CI). Attraction between the ions reduces the conducting ability of the ions, hence, Am falls with increasing concentration. But if solution is diluted (concentration is decreased) the ions, there will be a decrease in ionic attractions, hence, molar conductivity increases with decrease in concentration. Further, molar conductivity approaches a maximum limiting value at infinite dilution.
The plot for strong electrolyte becomes linear near at high dilution and can be extra ploted to zero concentration to get the value of Λm Λeq Molar conductivity at infinite dilution.
For Weak Electrolyte
In case of weak electrolytes (as CH₂COOH, NH, OH AgCl etc.), ionization is very small compared to strong electrolytes, hence, Λm (or Λeq) of a weak electrolyte is low. Thus, the conductance of weak electrolytes is less than that of strong electrolyte at the same concentration.
| Variation of A with C for weakly electrolyte (CH,COOH). A cannot be obtained by extrapolation of CO. |
The above curve clearly shows that there is a very large increase in the conductance on dilution because of increase in the number of ions in the solution due to an increase in the degree of ionization of weak electrolyte. The graph is not linear (in Fig) in lower concentration range and thus A cannot be obtained by extrapolation.
However, at infinite dilution when C → 0, although an electrolyte dissociates completely (a = 1) but at such low concentration the number of ions per unit volume is so low that, the conductivity of the solution cannot be measured accurately. The value of Λm for weak electrolytes is actually obtained by indirect method based on kohlrausch's law