# Experimental determination of transport number

- In today’s article, we are going to study about ‘Experimental determination of transport number’ and what is transport number and Hittorf’s method. How beneficial it is. We will also read about some more topics like Hittorf’s method, transport numbers, apparatus, determination of Transport number etc in detail. So, take your notebooks in you hand and get ready to study physics in an easy and sorted way.

There are methods for determination transport number experimentally. These are

- Hittorf’s Method
- Moving Boundary Method

## Hittorf’s Method

The principle of this method is based on the observed concentration change in the vicinity of the electrodes. As mentioned above,

Mobility of cation (U)/ Mobility of anion (V) = Fall of concentration around anode/ Fall of concentration around cathode …(1)

It means,

Fall of concentration around cathode ∝ U …(2)

Fall of concentration around anode ∝ V …(3)

Fall of concentration in both compartments ∝ U+V …(4)

On dividing equation (2) by equation (4)

Fall of concentration around anode/ Fall of concentration in both compartments = U/U+V …(5)

Similarly,

Fall of concentration around cathode/ Fall of concentration in both compartments = V/U+V …(6)

But we know that,

Transport number of cation nc = U/U+V

Therefore, nc = Fall of concentration around anode/ Fall of concentration in both compartments

If concentration is taken in gram equiv lit^-1, then

nc = Loss of gram equivalents around anode/ Total loss of gm equivalents in both compartments …(7)

But, total number of gram equivalents lost from both the compartments is equal to the number of gram equivalents deposited on each electrode.

Therefore, equation (7) can also be written as,

nc = Loss of number of gram equivalents around anode/ number of gram equivalents deposited on each electrode …(8)

## Theory-

Since, according to Faraday’s second law of gram equivalents deposited on each electrode must be equal to the number of gram equivalents of copper deposited in copper coulometer (or silver deposited in silver coulometer) by the same charge. Hence, It is more convenient to include either copper or silver coulometer in series with experimental electrolyte. And to find out the amount of either copper or silver deposited on the cathode. Therefore, equation (8) can also be written as,

nc = Loss of number of gram equivalents around anode/ Number of gram equivalents of copper deposited in the coulometer

Or

nc= Number of gram equivalents lost from the anode compartments/ Number of gram equivalents of copper deposited in the coulometer

Similarly

na = Number of gram equivalents lost from the cathode compartment/ Number of gram equivalents of copper deposited in the coulometer

Thus, in order to determine transport number by Hittorf’s Method one should known the loss of gram equivalents in either Cathodic or anodic compartment and total gram equivalents deposited in coulometer.

## The apparatus

A general diagram of Hittorf’s apparatus is shown in fig. It consists of two vertical glass tubes A and B connected through U-tube in the middle. Tubes A and B contain cathode and anode respectively and represent cathodic and anodic compartments while the U-tube represents the meddle Compartment. Each tube is provided with a stop cock at the bottom. Electrodes are sealed in narrow glass tubes which pass through rubber stoppers as shown in fig. Two stop cocks P and Q are also provided at the ends of middle tube. Which can be used to stops the flow of liquid between anodic and cathodic compartments.

Apparatusis filled with the solution of known concentration. Electrodes are fitted in tubes A and B and then these electrodes are connected in series with a copper (or silver) coulometer and a battery through a variable resistance. A milliammeter is also include in the circuit to read the current strength. A current of 0.10 to 0.02 ampere is passed for about 2 to 3 hours in the circuit so that an appreciable (not too large) change in the concentration around the electrodes may taken place.

After the experiment, solution is withdrawn from the electrodes as well as central compartment by opening stop cock at the bottom. The change of concentration in each solution is determined. There should be no change in the concentration of the solution withdrawn from the central compartment. If changes is observed in the concentration of central compartment experiment should be repeated. Metal deposited in coulometer is also determined. With the nature of electrodes different conditions may arise.

#### Conclusion

So our article is finished and after completely reading this article, one can easily tell what is Transport number and Hittorf’s method and experimental diagram to determine transport number.

So one can say that they got a detailed information about Hittorf’s method.

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