Molality and Activity

Molalities are an alternative way of expressing the composition of a mixture, rather than mole fractions.

The molality of a dissolved substance is expressed as the number of moles of the substance present per kilogram of solution.

We may thus introduce an another definition of activity (which follows on from those we have considered thus far) which will prove to be of use in various fields of chemistry (for example in considering the properties of ionic solutions). We are familiar with the definition of the mole fraction , which for the solute, B, in a two-component mixture is as follows:

where, as usual, nX is the amount of X in moles. However, in a dilute solution, the amount of solute is much less than the amount of solvent (nB <<  nA) which means that we can approximate the above expression with:

nB (the number of moles of B present) is proportional to bB, the molality of B (the number of moles of B per kg of solution). We may thus write:

where κ is a dimensionless constant. bº has the numerical value 1mol kg-1 , and is the defined molality of the solution in its standard state.  From an equation derived on the previous page, we may substitute the above expression for xB and obtain:

We now combine the first two terms on the right hand side of the equation and define this as a new standard chemical potential, μº. This gives

This equation indicates that the chemical potential of the solute has its standard value when the molality of B is equal to bº. Note that as the solution becomes diluted (as bB gets closer and closer to zero) the logarithm, and hence the chemical potential of the solution, becomes increasingly negative. This indicates that the solute is stabilised by increasing dilution, an effect which can be seen in the great difficulty that exists in removing the last traces of a solute from a solution.

As for the case of the solution, deviations from ideality may be incorporated in an activity, aB, which is related to the molality by an activity coefficient, γB, as follows:

All deviations in ideality are now included in the activity coefficient γB. We can then write the following expression, which gives the chemical potential of a real solute at any molality:

where the activity is as defined above.