ELECTRON CHEMISTRY

Kohlrausch’s law:

Kohlrausch’s law states that the equivalent conductivity of an electrolyte at infinite dilution is equal to the sum of the conductances of the anions and cations. If a salt is dissolved in water, the conductivity of the solution is the sum of the conductances of the anions and cations

\lambda^\infty _e_q = \lambda^\infty _c +\lambda^\infty _a

where,

\lambda^\infty _e_q =Equivalence\ Conductivity\ at\ Infinite\ Dilution

\lambda^\infty _c =Conductivity\ of\ Cation

\lambda^\infty _a =Equivalence\ Conductivity\ of Anion

According to Kohlrausch’slaw. “conductivity of ions is constant at infinite dilution and it does not depend on nature of co-ions.”

 

  • Calculation of Molar Conductivity at Infinite Dilution For Weak Electrolytes

As already mentioned, the molar conductivity  of weak electrolytes at infinite dilution cannot be determined experimentally, firstly because the conductance of such a solution is low and secondly because dissociation of such an electrolytes is not completed even at high dilutions.

The molar conductivity of such an electrolyte at infinite dilution can be calculated using Kohlrausch’s law

  • Calculation of Degree of Dissociation

According to Arrhenius theory of electrolytic dissociation, the increase in the molar conductivity with dilution is entirely due to the increase in the dissociation of the electrolyte; the molar conductivity at infinite dilution being maximum because the dissociation is almost complete.

Thus if \lambda ^c_m is the molar conductivity of a solution at any concentration C and \lambda _m^\infty the molar conductivity at infinite dilution (i.e. zero concentration), we will have

\alpha = \frac{no. of\ dissociated\ ions}{no.\ of\ total\ ions\ present}=\frac{\lambda _m^c}{\lambda _m^\infty }

However, this relationship is found to hold good only for weak electrolytes. The value of \lambda _m^\infty for the weak electrolytes can be calculated , using Kohlrausch’s law, as discussed already in the first application.

  • Calculation of Dissociation Constant For a Weak Electrolyte

Knowing the degree of dissociation (as calculated above) the dissociation constant (K) of the weak electrolyte at concentration C of the solution can be calculated

using the formula

K_c = \frac{C\alpha ^2}{1-\alpha }

  • Calculation of Solubility of Sparingly Soluble Salt

Salts such as AgCl. BaSO4, PbSO4 etc which dissolve to a very small extent in water are called sparingly soluble salts.

A they dissolve very little, their solutions are considered as infinitely dilute. Further as their solutions are saturated, their concentration is equal to their solubility.

Thus by determining the specific conductivity (K) and the molar conductivity of such solutions , we have

\lambda _m^o = \kappa \times \frac{1000}{Molarity} = \kappa \times \frac{1000}{Solubility}

\Rightarrow Solubility = \frac{\kappa \times 1000}{\lambda _m^o}

 

Interionic AttractionS:

This theory was discovered due to Arrhenius’s theory having deficiencies.

Interionic Attractions are when an ion is surrounded by an ionic atmosphere which has a net charge opposite for its own. For example an anion would be completely surrounded by ions mostly composed of cations and a cation would mostly be surrounded by ions of anions. The ionic atmosphere decreases the mobility of each ion by exerting a drag on it, which in turn also decreases the magnitude of colligative properties. The ionic atmosphere cannot created nor destroyed.

In solutions with weak electrolytes the number of ions is not large, therefore the effect of the interionic attraction is small. In a concentrated solution of strong electrolytes the ion count is large, and therefore the interionic attraction will be apparent. The reason behind the differences in the interionic attraction is that in concentrated solutions ions are closer together due to the large ion count, while in less concentrated solutions they are further apart.