Thermodynamic activity

In thermodynamics, activity (symbol $a$ ) is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution. The term "activity" in this sense was coined by the American chemist Gilbert N. Lewis in 1907.^[1]

By convention, activity is treated as a dimensionless quantity, although its value depends on customary choices of standard state for the species. The activity of pure substances in condensed phases (solids and liquids) is taken as $a$ = 1.^[2] Activity depends on temperature, pressure and composition of the mixture, among other things. For gases, the activity is the effective partial pressure, and is usually referred to as fugacity.

The difference between activity and other measures of concentration arises because the interactions between different types of molecules in non-ideal gases or solutions are different from interactions between the same types of molecules. The activity of an ion is particularly influenced by its surroundings.

Equilibrium constants should be defined by activities but, in practice, are often defined by concentrations instead. The same is often true of equations for reaction rates. However, there are circumstances where the activity and the concentration are significantly different and, as such, it is not valid to approximate with concentrations where activities are required. Two examples serve to illustrate this point:

In a solution of potassium hydrogen iodate KH(IO₃)₂ at 0.02 M the activity is 40% lower than the calculated hydrogen ion concentration, resulting in a much higher pH than expected.
When a 0.1 M hydrochloric acid solution containing methyl green indicator is added to a 5 M solution of magnesium chloride, the color of the indicator changes from green to yellow—indicating increasing acidity—when in fact the acid has been diluted. Although at low ionic strength (< 0.1 M) the activity coefficient approaches unity, this coefficient can actually increase with ionic strength in a high ionic strength regime. For hydrochloric acid solutions, the minimum is around 0.4 M.^[3]

^ Lewis, Gilbert Newton (1907). "Outlines of a new system of thermodynamic chemistry". Proceedings of the American Academy of Arts and Sciences. 43 (7): 259–293. doi:10.2307/20022322. JSTOR 20022322. ; the term "activity" is defined on p. 262.
^ Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002). General Chemistry (8th ed.). Prentice Hall. p. 804. ISBN 0-13-014329-4.
^ McCarty, Christopher G.; Vitz, Ed (2006), "pH Paradoxes: Demonstrating that it is not true that pH ≡ −log[H⁺]", J. Chem. Educ., 83 (5): 752, Bibcode:2006JChEd..83..752M, doi:10.1021/ed083p752

[1] Lewis, Gilbert Newton (1907). "Outlines of a new system of thermodynamic chemistry". Proceedings of the American Academy of Arts and Sciences. 43 (7): 259–293. doi:10.2307/20022322. JSTOR 20022322. ; the term "activity" is defined on p. 262.

[2] Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geoffrey (2002). General Chemistry (8th ed.). Prentice Hall. p. 804. ISBN 0-13-014329-4.

[McCarty2006-3] McCarty, Christopher G.; Vitz, Ed (2006), "pH Paradoxes: Demonstrating that it is not true that pH ≡ −log[H⁺]", J. Chem. Educ., 83 (5): 752, Bibcode:2006JChEd..83..752M, doi:10.1021/ed083p752

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