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I learned in class that the equivalence point is the point of neutralization where the amounts of acid and base are equivalent.

I was also told that the half-equivalence point is when the concentration of a weak acid equals concentration of conjugate base: $[\ce{HA}] = [\ce{A-}].$

I did a research and found similar definitions that don’t really shed any light on the differences between them and both terms seem identical to me. What is the difference between a half-equivalence and an equivalence point, exactly?

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    $\begingroup$ Look at the benzoic acid titration curve here: chemistry.stackexchange.com/a/117033/79678 . Halfway to the equivalence point, the concentration of benzoic acid equals that of benzoate ion. The is the middle of the buffer region. At the equivalence point, you just have a solution of sodium benzoate. There are lots of pH questions and answers here, so please use the search function. $\endgroup$
    – Ed V
    Feb 23, 2020 at 3:41
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    $\begingroup$ In short then the difference is striking. $\endgroup$
    – Alchimista
    Feb 23, 2020 at 8:55
  • $\begingroup$ Start with exactly 1 M HCl solution. Now add exactly 0.5 moles of solid NaOH. This is the half-equivalence point: half of the total HCl has been neutralized, resulting in a solution that is 0.5 M HCl (aq) and 0.5 M NaCl (aq). Note that chloride ion is the (pathetically weak) conjugate base of HCl (aq). Now add another 0.5 moles (exactly) of solid NaOH. This is the equivalence point: all of the acid and base have exactly neutralized and you have a 1 M NaCl solution with pH 7. Hope this helps. $\endgroup$
    – Ed V
    Feb 23, 2020 at 15:07
  • $\begingroup$ I assumed exactly 1 liter of the exactly 1 M HCl solution. Activities and auto-ionization of water are neglected. At the half-equivalence point, the molar concentrations of hydronium and sodium ions are each 0.5 M and the chloride concentration is 1 M. This is charge neutrality. At the equivalence point, the sodium and chloride ion concentrations are each 1M. The hydronium and hydroxide are the values at pH 7, i.e., 100 nM each. $\endgroup$
    – Ed V
    Feb 23, 2020 at 15:43

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The equivalence point is where the amount of moles of acid and base are equal, resulting a solution of only salt and water. If you are titrating an acid against a base, the half equivalence point will be the point at which half the acid has been neutralised by the base. For instance, if you have 1 mole of acid and you add 0.5 mole of base, exactly half of the acid will have been neutralised. The solution remaining will be half salt and half acid.

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Now I was also told that Half equivalence point is when [HA] = [A−] , the concentration of a weak acid = concentration of conjugate base.

That is correct. You make the weak acid in situ when you titrate a weak base with a strong acid, or when you titrate a weak acid with a strong base. At the half equivalence point, the pH is roughly equal to the pKa of the weak acid.

What is the difference between a half equivalence and an equivalence point?

The equivalence point is what it always is. The point when you added stoichiometric amounts of titrant to the analyte. In the weak acid / strong base case, it means that you have quantitatively turned the weak acid into weak base, and don't have any excess of strong base (all was neutralized). The pH would be that of the weak base. In the weak base / strong acid case, it means that you have quantitatively turned the weak base into weak acid, and don't have any excess of strong acid (all was neutralized). The pH would be that of the weak acid.

Based on what i have been told, they sound the same to me.

Compared to the equivalence point, you have to add half the titrant to reach the half equivalence point, so they are different.

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