The correct operational relationship between pKa and pH is that...

Question

BlackTom AI · Accepted Answer

Henderson–Hasselbalch equation: pH = pKa + log([A–]/[HA]).

1) Relevant knowledge points and concepts
- pKa is the negative log of the acid dissociation constant for an acid HA ⇌ H+ + A–; it quantifies the tendency to lose a proton.
- pH measures proton activity in solution.
- The Henderson–Hasselbalch equation links pH, pKa, and the ratio of deprotonated ([A–]) to protonated ([HA]) forms.
- When pH = pKa the ratio [A–]/[HA] equals 1, meaning equal amounts of protonated and deprotonated species.

2) Step-by-step reasoning
Start with Henderson–Hasselbalch:
pH = pKa + log([A–]/[HA]).
Set pH = pKa and solve for the ratio.

3) Calculations and intermediate steps
pH = pKa implies:
pKa = pKa + log([A–]/[HA])
=> 0 = log([A–]/[HA])
=> 10^0 = [A–]/[HA]
=> 1 = [A–]/[HA]
So [A–] = [HA]. Fraction protonated = [HA]/([HA]+[A–]) = [HA]/(2[HA]) = 1/2 = 50%. Fraction deprotonated = 50%.

4) Why the correct answer is correct
Because the algebraic consequence of the Henderson–Hasselbalch equation at pH = pKa is a 1:1 ratio of base to acid forms. That directly means the compound is half protonated and half deprotonated, independent of whether the species is an acid or the conjugate acid of a base (the same logic applies when using the conjugate acid’s pKa).

5) Why the other options are incorrect
- a: pKa and pH are not constrained to be <7 or >7 by acid/base labels; many weak acids have pKa >7 and pH depends on concentration and solution; the statement is false.
- b: pKa and pH are operationally related (Henderson–Hasselbalch) even in complex biological fluids; buffers use this relationship.
- d: “Charge of +0.5” is meaningless as net molecular charge is not a fractional single integer in that way; half protonation means 50% of molecules carry the protonated charge and 50% do not, not that each molecule has +0.5 charge.

6) Conclusion
Therefore the correct operational relationship is option c: when pH = pKa the species is half protonated and half deprotonated, matching the provided answer.

The correct operational relationship between pKa and pH is that...单项选择题

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