Activity is a new concept for me, and I am having a little bit of trouble understanding it.
For the equation:
$$\ce{aA + bB<=>cC + dD}$$
$$K_c= \frac{[\ce{A}]^a[\ce{B}]^b}{[\ce{C}]^c[\ce{D}]^d}$$
As I understand it, this is not the true equilibrium constant expression for the chemical equation above. My textbook calls $K_c$ in this instance the "concentration quotient." The technically correct equilibrium constant expression is:
$$K=\frac{(a_\ce{A})^a(a_\ce{B})^b}{(a_\ce{C})^c(a_\ce{D})^d}$$
Where $K$, in this equation, is the "true" equilibrium constant determined by the activity, $a$, of each species in equilibrium with each other. The activity is represented by the equation: $a_\ce{A}=\gamma_\ce{A} [\ce{A}]$, where $\gamma$ is the activity coefficient.
My textbook Quantitative Chemical Analysis (Ninth Edition, by Daniel C. Harris), states that "the equilibrium 'constant' is not really constant." And then it goes into how increasing ionic strength increases the solubility of ionic compounds in aqueous solution. It then later states "the activity coefficients must decrease with increasing ionic strength."
This would seem to contradict the idea that increasing ionic strength increases the solubility of an ionic compound, would it not? If the ionic strength increases the solubility of an ionic compound, then wouldn't that mean that the concentrations of the ions that make up that ionic compound would increase, and thus the activity coefficient, therefore, must increase to show an increase in activity, otherwise known as the "effective concentration?"
Or is the activity independent of the ionic strength such that in order to keep the activity the same under higher concentrations, the activity coefficient must be smaller? This would then bring up the question: is the equilibrium constant, $K$, (determined by the activities of the components in the equilibrium expression) constant even under different ionic strengths, while the "concentration coefficient" (determined merely by the concentrations of the components in equilibrium with one another) does vary under different ionic strengths? I'm not sure I'm getting this very well.