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

Question

BlackTom AI · Accepted Answer

When pH = pKa, the Henderson–Hasselbalch relationship directly gives the protonation ratio.

1) Relevant knowledge points and concepts
- pKa is the negative logarithm of the acid dissociation constant (Ka) and characterizes the tendency of an acid to donate a proton.
- pH is the negative logarithm of the hydrogen ion concentration.
- The Henderson–Hasselbalch equation links them: pH = pKa + log([A−]/[HA]), where [A−] is the deprotonated form and [HA] the protonated form (for a monoprotic acid). This applies similarly for ionizable bases when written in their conjugate acid/base form.

2) Step-by-step reasoning
Start from the Henderson–Hasselbalch equation:
pH = pKa + log([A−]/[HA])

Set pH = pKa:
pKa = pKa + log([A−]/[HA])

Subtract pKa from both sides:
0 = log([A−]/[HA])

3) Intermediate calculation steps
From 0 = log([A−]/[HA]), take the antilog (base 10):
10^0 = [A−]/[HA]
1 = [A−]/[HA]

Thus [A−] = [HA].

4) Why the correct answer is correct
The algebra shows that when pH equals pKa, the concentrations of the deprotonated and protonated forms are equal — i.e., the species is half protonated and half deprotonated. This is the operational meaning of pKa relative to pH and is true for any simple ionizable group described by the Henderson–Hasselbalch equation.

5) Why the other options are incorrect
a. “Charge of +0.5” is meaningless: molecular charge is not expressed as fractional integers like +0.5 and depends on the species’ actual protonation states and other ionizable groups, not simply pH = pKa. 
b. Claiming no operational relation is false because pKa and pH are directly related by the Henderson–Hasselbalch equation and determine protonation state.
d. “Both are always <7 for acids, and >7 for bases” is incorrect: pKa values can be above or below 7 depending on the acid; pH is the environment’s proton concentration and need not correlate in that absolute way.

6) Conclusion
Therefore the correct choice is c: When pH = pKa, the ionizable compound will be half protonated and half deprotonated, which matches the given answer.

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

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