What is the difference between equivalence and half-equivalence points?

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?




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.
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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.



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



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