# Conductance of Electrolytic Solutions

**Conductance of Electrolytic Solutions**

*Resistance (R)–*

- · Resistance is a measure of its opposition to the flow of electric current.
- · Si unit - ohm

*Resistivity-*

- · Resistivity is the characteristic property of the material by which it resists the amount of current through it.
- · Symbol- ρ
- · Si unit-ohm m

*Electrical conductance (G)*

- · The conductance is the property of the conductor (metallic as well as electrolytic) which facilitates the flow of electricity through it. It is equal to the reciprocal of resistance, i.e.,
- · Conductance = 1 / Resistance
- · It is expressed in the unit called reciprocal ohm (ohm
^{-1}or mho) or siemens.

*Specific conductance- *

- · The reciprocal of specific resistance is termed the specific conductance or it is the conductance of one centimeter cube of a conductor.
- · It is also called conductivity.
- · It is denoted by k or
- · $k=\frac{l}{A}\times C$

· where $\frac{l}{A}$ is the cell constant and C is the conductance.

**Molar conductance-** The molar conductance is defined as the conductance of all the ions produced by ionization of 1g mole of an electrolyte when present in V ml of solution. It is denoted by ${\lambda}_{m}$.

${\lambda}_{m}$ = $\frac{k\times 1000}{c}$

where ${\lambda}_{m}$ is molar conductance in $Sc{m}^{2}mo{l}^{-1}$, k is specific conductance in $Sc{m}^{-1}$ and is concentration in $mol{L}^{-1}$.

**Measurement of the Conductivity of Ionic Solutions**

To measure the conductivity of an ionic solution, we need an apparatus called a conductivity cell. A conductivity cell consists of two electrodes (usually platinum) of equal area and placed parallel to each other with a fixed distance between them. The cell is filled with the solution of the electrolyte whose conductivity is to be measured.

The conductivity cell is connected to a source of alternating current of known frequency and potential difference. The electrodes act as terminals to pass the current through the solution.

The cell also contains a device called a conductivity bridge which measures the resistance of the solution. The resistance of the solution can be measured by comparing it with a known standard resistor of the same value.

Once the resistance is measured, the conductivity can be calculated using the relation:

κ = G × l/A

where κ is the conductivity of the solution, G is the conductance of the solution (which is the reciprocal of the resistance measured), l is the distance between the electrodes, and A is the area of the electrodes.

The conductivity of the solution is measured in S/m, and the results are usually reported at a standard temperature of 25°C. It is important to note that the conductivity of a solution depends on the concentration of the electrolyte in the solution.

The conductivity cell can also be used to measure the molar conductivity of an electrolyte solution. The molar conductivity of an electrolyte is defined as the conductivity of the solution when one mole of the electrolyte is dissolved in one litre of the solution. The molar conductivity is represented by the symbol Λm and is measured in S m2 mol^{–1} or S cm^{2} mol^{–1}.

The molar conductivity of an electrolyte solution can be calculated using the relation:

Λm = κ × V/c

where V is the volume of the solution in litres, and c is the concentration of the electrolyte in moles per litre. The molar conductivity of an electrolyte solution varies with the concentration of the electrolyte, and the limiting molar conductivity is the molar conductivity of the electrolyte at infinite dilution (when the concentration of the electrolyte approaches zero).

In summary, the conductivity of ionic solutions can be measured using a conductivity cell and a conductivity bridge. The conductivity of the solution depends on the concentration and nature of the electrolyte and the temperature of the solution. The molar conductivity of the electrolyte can also be measured using the same setup, and it varies with the concentration of the electrolyte.

**Variation of Conductivity and Molar Conductivity with Concentration**

- Both conductivity and molar conductivity decrease with decrease in concentration, for both weak and strong electrolytes.
- Conductivity of a solution at a given concentration is the conductance of one unit volume of solution kept between two platinum electrodes with unit area of cross section and at a distance of unit length.
- Molar conductivity of a solution at a given concentration is the conductance of the volume V of solution containing one mole of electrolyte kept between two electrodes with area of cross section A and distance of unit length.
- Molar conductivity increases with decrease in concentration because the total volume of solution containing one mole of electrolyte increases.
- Molar conductivity at zero concentration is known as limiting molar conductivity (Λ°m).
- The variation in Λm with concentration is different for strong and weak electrolytes.
- For strong electrolytes, Λm increases slowly with dilution and can be represented by the equation Λm = Λ°m – A c
^{ ½}. - If we plot Λm against c
^{1/2}, we obtain a straight line with intercept equal to Λ°m and slope equal to ‘–A’. - The value of the constant ‘A’ for a given solvent and temperature depends on the type of electrolyte, which is determined by the charges on the cation and anion produced on the dissociation of the electrolyte in the solution.
- Electrolytes of the same type have the same value of ‘A’.

**Kohlrausch law**

· For an infinite dilution, equivalent conductivity of a weak electrolyte is equal to the sum of conductivity of the two types ion.

·

· For example, limiting molar conductivity, Λ of sodium chloride can be determined with the knowledge of limiting molar conductivities of sodium ion and chloride ion.

·

*Electrolytes*

· Substances which allow the electricity to pass through them in their molten or aqueous solution are called electrolytes.

**Types of Electrolytes**

*Strong Electrolyte –*

· Strong electrolytes are compounds that completely dissociate into its ions when dissolved in water.

· It Includes strong acids, strong bases, and some salts

· Example – sodium chloride, potassium chloride.

*Weak electrolyte –*

· Weak electrolytes are compounds that partially dissociate into its ions when dissolved in water.

· It includes weak acids, weak bases, and some salts.

· Example – acetic acid