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I hope to clear up some confusion I have about acid-base reactions in aqueous solution.

Based on the Bronsted-Lowry definition of acids, I know acids donate protons. In water, a strong acid should react completely with water to form hydronium and some anion. For example,

$\ce{HCl + H2O -> H3O+ + Cl-}$

However, my confusion arises when this acidic solution is reacted with another solution. For purposes of demonstration, I’ll use aqueous $\ce{NaOH}$. Usually, the acid-base reaction is

$\ce{HCl + NaOH -> H2O + NaCl}$

How is this possible if the $\ce{HCl}$ already reacted with water to form hydronium and chloride ions? Is it perhaps better to think of it in the Arrhenius sense where the original reaction is just $\ce{HCl -> H+ + Cl-}$ that way $\ce{HCl}$ can still be a reactant in the acid-base reaction without already being “used up”?

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The proton transfers may happen in cascade.

For example, pure $\ce{HCl}$ is a gas that dissolves and reacts with water (acting as a base) according to a proton transfer from HCl to $\ce{H2O}$ : $$\ce{HCl + H2O -> H3O+ + Cl- ... \ (1)}$$ But $\ce{H2O}$ does not hold its proton very strongly. Here is why : if another base like ammonia is added to this solution, a new proton transfer occurs from $\ce{H3O+}$ to $\ce{NH3}$ which is a stronger base than $\ce{H2O}$ $$\ce{H3O+ + NH3 -> NH4+ + H2O} ... (2). $$ A last proton transfer happens from $\ce{NH4+}$ to $\ce{OH-}$ if some solution of $\ce{NaOH}$ (containing $\ce{OH-}$ ions) is added, according to : $$\ce{NH4+ + OH- -> NH3 + H2O} ...\ (3) $$

This shows that

  • $\ce{H2O}$ is a base just strong enough to pick a proton from $\ce{HCl}$, according to ($1$).
  • $\ce{NH3}$ is a stronger base as it is able to pick up a proton form $\ce{H3O+}$ according to $(2)$. Of course $\ce{NH3}$ is also able to pick a proton for from $\ce{HCl}$, although it was not shown in the preceding cascade of events. But if pure $\ce{HCl}$ and pure $\ce{NH3}$ are mixed, the following proton transfer happens from $\ce{HCl}$ to $\ce{NH3}$ direct : $\ce{NH3 + HCl -> NH4+ + Cl-}$
  • $\ce{OH-}$ is the strongest base of all, as it is able to pick up a proton from $\ce{NH4+}$ as seen in (${3}$).

Of course, $\ce{OH-}$ is also able to pick up a proton from $\ce{H3O+}$ and $\ce{HCl}$

Just before the end, I would like to state that some teachers are reluctant to accept the reaction $({1})$, because nobody is sure that $\ce{H3O+}$ does exist. It could be admitted that the reaction is more complicated and does happen according to $\ce{HCl + 2 H2O -> H5O+ + Cl-}$ or even $\ce{HCl + n H2O -> H_{2n+1}O+ + Cl-}$. So, in order to simplify their teaching, they would recommend to simply write down the equation of $\ce{HCl}$ with water as : $\ce{HCl -> H_{aq}^+ + Cl-}$ And indeed the reaction of $1$ mole $\ce{HCl}$ with $2$ moles $\ce{H2O}$ is more exothermic that the reaction with $1$ mole $\ce{H2O}$.

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