To understand what happens beyond the end-point of a titration involving acetic acid ([tex]\(HC_2H_3O_2\)[/tex]) and sodium hydroxide ([tex]\(NaOH\)[/tex]), we should consider the stoichiometry and the nature of the substances involved.
Let's analyze the titration process step-by-step:
1. Equation and Reaction:
The balanced chemical equation is:
[tex]\[
HC_2H_3O_2(aq) + NaOH(aq) \longrightarrow NaC_2H_3O_2(aq) + H_2O(l)
\][/tex]
Here, acetic acid ([tex]\(HC_2H_3O_2\)[/tex]) reacts with sodium hydroxide ([tex]\(NaOH\)[/tex]) to produce sodium acetate ([tex]\(NaC_2H_3O_2\)[/tex]) and water ([tex]\( H_2O\)[/tex]).
2. Titration End-Point:
The end-point of the titration is reached when the amount of [tex]\(NaOH\)[/tex] added is stoichiometrically equivalent to the amount of [tex]\(HC_2H_3O_2\)[/tex] present. At this point, all of the [tex]\(HC_2H_3O_2\)[/tex] has been neutralized by [tex]\(NaOH\)[/tex], and the solution contains [tex]\(NaC_2H_3O_2\)[/tex] (which is a salt of the weak acid [tex]\(HC_2H_3O_2\)[/tex]) and water.
3. Beyond the End-Point:
Beyond the end-point, excess [tex]\(NaOH\)[/tex] has been added to the solution. This means there is a surplus of [tex]\(OH^-\)[/tex] ions because [tex]\(NaOH\)[/tex] dissociates completely in water:
[tex]\[
NaOH(aq) \rightarrow Na^+ (aq) + OH^- (aq)
\][/tex]
4. pH Consideration:
As [tex]\(NaOH\)[/tex] is a strong base and it dissociates completely, the excess [tex]\(OH^-\)[/tex] ions will increase the alkalinity of the solution. In other words, beyond the end-point, the concentration of [tex]\(OH^-\)[/tex] ions will be greater than the concentration of [tex]\(H^+\)[/tex] ions, leading to a basic or alkaline solution.
Given these points, beyond the end-point of titration, the correct statement about the relative concentrations of hydrogen ions ([tex]\(H^+\)[/tex]) and hydroxide ions ([tex]\(OH^-\)[/tex]) is:
[tex]\[
\left[ H ^{+}\right] < [ OH^- ]
\][/tex]
This means the solution is basic beyond the end-point because there are more hydroxide ions than hydrogen ions present.
