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21 Mar 2020
The following figure represents solutions at various stages of the titration of a weak acid, HA, with NaOH. (The Na+ ions and water molecules have been omitted for clarity.) To which of the following regions of the titration curve does each drawing correspond: (a) before addition of NaOH, (b) after addition of NaOH but before the equivalence point, (c) at the equivalence point, (d) after the equivalence point?
![](data:image/png;base64,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)
The following figure represents solutions at various stages of the titration of a weak acid, HA, with NaOH. (The Na+ ions and water molecules have been omitted for clarity.) To which of the following regions of the titration curve does each drawing correspond: (a) before addition of NaOH, (b) after addition of NaOH but before the equivalence point, (c) at the equivalence point, (d) after the equivalence point?
Irving HeathcoteLv2
23 May 2020