# Nernst Distribution Law

The distribution law or law of distribution , is defined when a substance is distributed between two immiscible liquids with one another or slightly miscible, and the ratio of the concentrations of said substance in the two phases is constant regardless of the amount of solute to dissolve or the volume of liquid used. This law was raised by Walther Nernst in 1931 .

## Summary

[ hide ]

• 1 Exemplification of the law
• 2 Limitations of the distribution law
• 3 Distribution of benzoic acid in water and benzene
• 4 Practical applications of the law of distribution
• 5 Sources

## Exemplification of the law

When analyzing how a solid or liquid substance is distributed between two non-miscible or partially miscible liquids, it is observed that this distribution is not verified randomly, but according to a certain regularity; Let’s analyze some experimental results at 250C to discover these regularities:

If a mass of mercury (II) bromide (HgBr2) in a mixture of C6H6 ( benzene ) and water (H2O) is shaken in a separating funnel , and the same is done with a certain mass of diiodine (I2) in a mixture of carbon tetrachloride (CCl4 and H2O), as well as dibromo (Br2) in a mixture of tribromomethane , (CHBr3 and H2O), we obtain the results shown in Figure No. 1:

Fig. 1. Experimental data verifying the distribution law.

As can easily be seen, the ratios of the concentrations of HgBr2 in water and carbon tetrachloride, and of Br2 in water and tribromomethane, are constant within the experimental error, which leads to the statement of this regularity known as the distribution law. or the distribution as follows:

If a solute is added to a system made up of two non-miscible liquids in contact, the whole is stirred to promote the mixture of the three substances and then it is left in process so that the two liquid layers separate again (until the equilibrium of distribution), it is found that the solute, for a given temperature, is distributed between the two non-miscible solvents, such that the ratio between their concentrations in one and the other solvent, is a constant amount, regardless of the mass of solute added and called constant or coefficient of the distribution.

The above should be expressed, for each system in the table above, as follows:

• The partitioning constant for HgBr2 at 250 C between water and benzene is 0.90.
• The constant of the distribution of I2 at 250 C between CCI4 and H2O is 85.2.
• The constant of the distribution of Br2 at 250 C between tribromomethane and water is 66.7

It is evident that no further explanation is required and that the constants are dimensionless; concentrations generally expressed in mass concentrations.

## Limitations of the distribution law

• The law is strictly valid for dilute solutions.
• If one of the solvents is saturated it is solute, it will undoubtedly not be able to dissolve more mass of said solute, so that if the other solvent is not saturated, the relationship between the concentrations will not be constant.
• If the solute is associated or dissociated in one solvent and is not in the other, that is, it does not have the formula-mass corresponding to a simple structure in both solvents, the relationship between the concentrations will not be constant.

## Distribution of benzoic acid in water and benzene

Fig. 2. Distribution of benzoic acid in water and benzene.

As seen in Fig 2, the distribution law is not fulfilled; but we proceed to calculate [C1 / C2] ½ and place it in the previous table: I imagined a solute X that is in the form of simple molecules, in solvent A, but that constitutes associated molecules Xn in solvent B, obviously there will be equilibrium Xn nX and in the above circumstances it can be proved that:

In the case of benzoic acid tabulated above, it can be stated that it is dimerized in the benzene solution, but not in the aqueous solution , so its formula in benzene equal to (C6H5COOH) 2 and in water must be considered C6H5COOH.

## Practical applications of the law of distribution

In substance extraction processes, when an active ingredient is to be extracted from a plant, the use of the volume of the solvent must be divided into several portions and repeat the process several times, this will cause more active ingredient to be extracted from the plant.

In the process of rinsing clothes if you have, say 10 l of water, it is better to divide the liquid into 5 parts, and rinse the clothes 5 times, than to say at once to use 10 liters.