# Question regarding chemical equilibrium when adding a salt to acid solution

Having read the following was wondering something: $$\mathrm {p}K_\mathrm{a} = -\log\frac{[\ce{H+}]_\mathrm{eq}[\ce{A-}]_\mathrm{eq}}{[\ce{HA}]_\mathrm{eq}}$$ $$\ce{HA <=> H+ + A-}$$ $$\mathrm{pH = p}K\mathrm{_{a}} +\mathrm{log\frac{[\ce{A-}]}{[\ce{HA}]}}$$ This rmgd $$\mathrm{[\ce{A-}] = [salt] }$$ when acid is weak.

Now my question is like this: take a beaker of $$\ce{CH3COOH}$$. Now add $$\ce{CH3COONa}$$. Now here using the a over formula as salt concentration increases $$\mathrm{pH}$$ should decrease when take in $$\ce{A-}$$ as salt concentration. However this same $$\ce{A-}$$ was there in the $$\mathrm{p}K_\mathrm{a}$$ formula so shouldn't the $$\mathrm{p}K_\mathrm{a}$$ change to compensate? If so then there will be no $$\mathrm{pH}$$ change but I have read that there is $$\mathrm{pH}$$ change on adding $$\ce{CH3COONa}$$ in a solution. What is wrong with this?

• The first equation is wrong : it’s Ka or not pKa – Nicolas Mar 1 at 13:16
• It is now editted . – ask Mar 1 at 13:23
• The first equation only works if the system is in equilibrium. I added to subscripts to indicate that. – Karsten Theis Mar 1 at 19:17
• indeed @KarstenTheis, I corrected my answer as well – Nicolas Mar 1 at 20:39

1. the second relation is wrong to : $$pK_{a} = -\log\frac{[\ce{H+}]_{eq}[\ce{A-}]_{eq}}{[\ce{HA}]_{eq}}=-\log[\ce{H+}]_{eq} -\log\frac{[\ce{A-}]_{eq}}{[\ce{HA}]_{eq}}$$ so $$pH=pK_a+\log\frac{[\ce{A-}]_{eq}}{[\ce{HA}]_{eq}}$$
2. the acidity constant is the relation which links the concentrations of the species present (and not the reverse): if we add the salt $$\ce {A^-}$$, then according to the relation you see that the pH increases. You can also see it by reasoning thus: you add a base so the pH can only increase.