# Conductivity

According to Ohm’s law, the strength of current, C flowing through a conductor of resistance, R is directly proportional to the potential difference E, applied across the conductor. This statement may be represented by;

$E = CR \hspace{2mm} or \hspace{2mm} C = \dfrac{E}{R}$

The current is measured in ampere, the potential difference in volt and the resistance in ohm. The reciprocal of resistance, R, is known as conductance or electrical conductivity and is expressed in units of reciprocal ohm(r, 0) ohms inverse $(ohm^{-1})$ mhos or Siemen (S).

Specific conductivity

Ohm’s law is also valid to electrolytic solutions. Thus the resistance R offered by an electrolyte to the passage of electricity is proportional to the length I and inversely proportional to the area of across solution, a of the column of the electrolyte lying between the electrodes.

Therefore, $R \propto \dfrac{1}{2} \hspace{2mm} or \hspace{2mm} R = \rho \times \dfrac{1}{a}$

a where p is a constant called resistivity or specific resistance, defined as the resistance offered by one $cm^3$ of the metal. The reciprocal of specific resistance is known as specific conductivity. Thus substituting the terms conductivity and specific conductivity in place of resistance and specific resistance, in the above expression, we have

$\dfrac{1}{\text{Obs. Conductivity}} = \dfrac{1}{\text{Sp. Conductivity}} \times \dfrac{1}{a}$

$or \hspace{2mm} \text{Sp. Conductivity = Obs. Conductivity} \times \dfrac{1}{2}$

$or \hspace{2mm} \text{Sp. Conductivity} = \text{ObS. Conductivity} \times \text{Cell constant}$

$K_v \hspace{2mm} or \hspace{2mm} k(\text{Specific conductivity} = C \times \dfrac{1}{a}$

The ratio 1/a is constant for a particular conductivity cell and is known as cell constant and is denoted by x. If I 1 cm and $a = 1 cm^2$, then

Specific conductivity = Conductivity

Thus specific conductivity may be defined as: “The conductivity of one $cm^3$ of the solution of electrolyte is called specific conductivity”.

Equivalent conductivity

Equivalent conductivity may be defined as: “The conductivity of the solution containing one equivalent of the electrolyte when placed between two sufficiently large electrodes kept one cm apart”.

It is denoted by the symbol $\lambda_v$ (lambda); where V is the volume in mL containing one equivalent of the solute. The equivalent conductivity is also related with specific  conductivity $K_v$ and the volume V in mL containing one equivalent of the electrolyte, as:

$\Lambda_v or \lambda_v = K_v \times V$

$or \Lambda_v or \lambda_v = \dfrac{1000K_v}{N} ohm^{-1} cm^2 eq^{-1}$

Molar conductivity

Sometimes, the term, molar conductivity is used for comparison among different electrolytes. This may be defined as: “The conductivity of a solution containing one mole of the electrolyte when placed between two sufficiently large electrodes kept one cm apart”.

It is denoted by the symbol $\mu_v$ (mew) where V is the volume in mL containing one mole of the soulte. Similar to equivalent conductivity, molar conductivity is also related with specific conductivity as:

$\Lambda_m or \mu_v = K_v \times V$

$\Lambda_m or \mu_v = \dfrac{100 K_v}{M} ohm^{-1}cm^2 mole^{-1}$

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