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From Practical skills in Biology by Allan Jones et al.

At high concentrations of certain ionic solutes, $\gamma$ (activity coefficient) may increase to become greater than unity.

My questions : If activity coefficient $\gamma$ $=$ $ {a}/{[C]} $ where $a$ is activity which signifies effective concentration and $[C]$ is concentration, how can $a$ be greater than $[C]$ ?

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A) Gamma < 1 means attractive forces dominate, and there is a decrease of vapour pressure of solute A relative to pure A. B) Gamma > 1 means repulsive forces dominate, and there is an increase of vapour pressure of solute A relative to pure A. You can think of activity coefficients as a qualifier for "escaping tendency" of the solute. With case A) above, the partial molar excess Gibbs energy of mixing is negative, meaning the solvent stabilises the solute, and energy is given away as a result of the mixing event (i.e. mixing is spontaneous). With case B) above, the partial molar excess Gibbs energy of mixing is positive meaning the solvent destabilises the solute, and energy is required in order to achieve mixing (i.e. mixing is NOT spontaneous). Think of activity as escaping tendency - a small activity means the solute remains in the solvent due to attractive forces whereas a large activity indicates a large escaping tendency of the solute because repulsive forces dominate. a = gamma x [conc.], right? So, if gamma > 1, then a is going to be larger than [conc.]. It might help you to consider fugacity, which is the analogue of activity for gases (which employs similarly the fugacity coefficient). Also consider an aqueous solution of ammonium hydroxide. You make it to be X M, right? But you can always smell ammonia since the solution you made is losing quantities of ammonia. Is the gamma for NH3 > or < than 1?

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In chemical 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.

(From Wikipedia.)

So the main point is that that activity is just a measure of the deviation from the ideal solutions, because the laws you are using in physical chemistry assume that solution is ideal. But usually it is not true. Laws can work for real life with a certain precision, but you should always remember about their "ideality" and the non-ideality of our world.

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    $\begingroup$ Hi! Thank you for your input. But I still don't understand how gamma can be greater than 1. $\endgroup$ – biogirl Feb 22 '14 at 2:24
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What is meant by effective concentration is whatever number makes the equilibrium equation work. To a first approximation it is true that, for example, [Na$^+$][Cl$^-$] is a constant in any solution saturated with NaCl at a given temperature, regardless of whatever else might be in the solution; but if you add lots of HCl, although [Na$^+$] does go down as [Cl$^-$] goes up, the product is not exactly constant. You can tabulate values for each concentration that will make the product constant, and these are called activities. As @Gordon Driver mentioned, these values can be either greater or less than the actual concentration, depending on the specific system.

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