Molecular Weight Of Substances In Solutions : Activity Theory Of Strong Electrolytes

The newer theory of electrolytes puts a different interpretation on these results, since it assumes that in solutions of the concentrations given in the table the ionisations are practically complete, and hence a has not the meaning attributed to it above. The variations in conductivity are assumed to be due to changes in mobility of the ions owing to the electrical forces exerted upon each ion by other ions of opposite sign. The changes in osmotic pressure (and therefore of freezing point) are also regarded as due to the varying attractions exerted between the ions, which at higher concentrations cause the osmotic pressure to have too small a value in the same way as the attractions between gas molecules at higher pressures cause a diminution of pressure on the walls of the vessel. On the new theory, the osmotic coefficient (D - Λ) / Λ (x - 1), and the conductance ratio, Λ / Λ_∞ are not exactly but only approximately equal. Just as the change in equivalent conductivity is explained by varying mobility of the ions with concentration, so the variations of the osmotic effect are correlated by changes of activity of the ions with concentration, the number of ions remaining the same in both cases.

Let P_i be the osmotic pressure calculated on the assumption that the electrolyte is completely ionised and obeys the gas laws, i.e., for a binary electrolyte P_i = 2cRT. On account of the interiomc attraction the observed osmotic pressure P is less than P_i, but becomes equal to it at infinite dilution. Let

, (1)

where f₀ is the osmotic coefficient, which becomes 1 in very dilute solution when θ vanishes. Equation (1) holds with D_i and D, or E_i and E the ideal and observed depressions of freezing point, or elevations of boiling point, on the assumption of complete ionisation, as well as with P_i and P, since these are proportional, quite independently of any theory of solutions.

The value of θ, therefore, represents the deviation from the ideal gas laws exhibited by the ions in solution. The theory of Debye and Hückel shows that for an electrolyte giving two ions of unit charge (B⁺ + A^-), at a total molar concentration c:

. (2)

For water at 0° C. as solvent the value of β is 0.372. It is convenient to introduce another coefficient, called the activity coefficient, f, defined as

. (3)

a being the activity of the dissolved substance. Then the Debye-Hückel theory leads to the relation, for an electrolyte of the type considered:

. (4)

where log_{e_{is the natural logarithm, equal to 2.3026 times the logarithm to the base 10. For water at 25° C. as solvent the value of β is 0.384

We must remember that the simple interpretation of Λ / Λ_∞ the conductivity ratio, as giving the degree of ionisation a, no longer holds in the new theory, nor does the relation of this to the osmotic pressure etc. take the form previously deduced. Instead we must introduce a new conductivity coefficient:

. (5)

Debye and Hückel's theory now shows that, for an electrolyte B⁺A^- we have:

, (6)

agreeing with experiment as far as the linear dependence of Λ on √c in very dilute solutions is concerned, as previously seen. It must be kept in mind that (5) and (6), like (1), (2) and (3), imply that the electrolyte is completely ionised. Debye and Hückel's theory states further that the constants β and K are independent of the composition of the electrolyte B⁺A^-, but depend only on the solvent and the temperature.}}

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Molecular Weight Of Substances In Solutions
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