A question relating to equilibrium concentrations for weak acids?

Question

Basically, I need an explanation of what's going on here. It's a part of a chapter that explains the concept of dissocation constants for acids and bases. 


Consider a weak acid HX that is partially ionized in the aqueous solution. The equilibrium can be expressed by:
HX (aq) + H2O (l) <----> H3O+ (aq) + X- (aq)
If the initial  concentration of the acid is "c", and "α" is the extent of ionization, after dissociation of the acid, at equilibrium, the equilibrium concentration of the acid HX is c-cα and that of H3O+ and X- is cα                      

How did they figure out the equilibrium concentrations of the acid as c-cα?

docrider28 · Accepted Answer

Because c is the initial concentration of the acid and α is the extent of ionization, the product cα is the amount of HX that has ionized and is no longer part of HX. One might also write it as HX -cα.  It follows then that the amount of H3O+ is equal to the ionized portion of HX or cα and it is also the concentration of X-.
[H3O+](aq)  = cα
[X-](aq) =cα
[HX)(aq) = c -cα

Think of alpha "α" as the fraction of c that is ionized.

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A question relating to equilibrium concentrations for weak acids?

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