For weak acids, percentage dissociation is

Question

BlackTom AI · Accepted Answer

For a weak acid HA dissociating as HA ⇌ H+ + A-, the equilibrium constant and percent dissociation determine the relationship with concentration.

1) Relevant concepts
- Acid dissociation constant Ka = [H+][A-]/[HA].
- If initial concentration is c and dissociation at equilibrium is x, then [H+] = [A-] = x and [HA] = c − x.
- Percent dissociation = (x/c) × 100%.

2) Step-by-step reasoning
Write Ka in terms of c and x:
Ka = x·x/(c − x) = x^2/(c − x).

For a typical weak acid x << c, so c − x ≈ c. Then
Ka ≈ x^2/c.

Solve for x:
x ≈ sqrt(Ka · c).

Percent dissociation (fractional form) = x/c ≈ sqrt(Ka · c)/c = sqrt(Ka)/sqrt(c)/ = sqrt(Ka/c).

3) Intermediate steps shown
- Ka ≈ x^2/c → x ≈ (Ka·c)^(1/2).
- x/c ≈ (Ka·c)^(1/2)/c = (Ka)^(1/2) / (c)^(1/2) = sqrt(Ka/c).

4) Why the correct answer is correct
The fractional dissociation ∝ 1/√c, so percent dissociation decreases as the initial acid concentration increases. This is an inverse relationship with concentration (more precisely, inverse square-root dependence). Thus percent dissociation is inversely related to acid concentration.

5) Why other options are incorrect
- b (always constant): incorrect because percent dissociation changes with concentration and Ka.
- c (not affected by acid concentration): incorrect; we just derived dependence on c.
- d (directly proportional to acid concentration): incorrect because increasing c lowers percent dissociation, not increases it.

6) Conclusion
Therefore the correct choice is (a) inversely proportional to acid concentration, which matches the provided answer.

For weak acids, percentage dissociation is单项选择题

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