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AP Chemistry Notes

8.10.1 Concentration vs capacity at constant ratio

AP Syllabus focus: ‘Increasing the concentrations of buffer components while keeping their ratio constant keeps pH the same but increases the buffer’s capacity to neutralize added acid or base.’

Buffers are designed to keep pH nearly constant during small acid/base disturbances. This page focuses on why pH depends on a ratio of buffer components, while buffer capacity depends on their absolute concentrations.

The key comparison: pH vs buffer capacity

pH is controlled by a concentration ratio

A typical buffer contains a weak acid and its conjugate base (or a weak base and its conjugate acid). For an acid buffer, the pH is set primarily by the ratio [A]/[HA][A^-]/[HA], not by the absolute size of each concentration.

Buffer capacity: the amount of strong acid or strong base a buffer can neutralise before its pH changes by a significant amount.

Keeping the ratio constant means both components are scaled up or down together (for example, doubling both [HA][HA] and [A][A^-]).

Henderson–Hasselbalch (acid buffer)=pH=pKa+log!([A][HA]) \text{Henderson–Hasselbalch (acid buffer)} = pH = pK_a + \log!\left(\frac{[A^-]}{[HA]}\right)

pH pH = acidity of the solution (unitless)

pKa pK_a = logKa-\log K_a for HAHA (unitless)

[A] [A^-] = molar concentration of conjugate base (M)

[HA] [HA] = molar concentration of weak acid (M)

If [A][A^-] and [HA][HA] are both multiplied by the same factor, the fraction [A][HA]\frac{[A^-]}{[HA]} is unchanged, so the pH stays the same (assuming ideal behaviour).

Buffer capacity is controlled by total “inventory” of acid/base

Even if two buffers have the same ratio (and thus the same starting pH), they can behave very differently when challenged. Buffer capacity increases when the actual concentrations (and therefore moles present) increase, because there is more material available to react with added H3O+H_3O^+ or OHOH^-.

Capacity is a stoichiometric idea: added strong acid or base is consumed mainly by the buffer components, and the pH shift occurs because their ratio changes.

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Titration curve for an acetic acid/acetate buffer during addition of strong base (NaOH). The gently sloping portion corresponds to the effective buffering region, where pH changes slowly because both HAHA and AA^- are present in appreciable amounts. The sharp rise indicates the buffer capacity has been exceeded and the pH becomes much more sensitive to added base. Source

Why increasing concentration increases capacity (at constant ratio)

What happens when strong acid is added

For an acid buffer HA/AHA/A^-, added H3O+H_3O^+ is consumed mostly by the conjugate base:

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Schematic “before vs after” diagram for an acetic acid/acetate buffer showing how the conjugate-pair amounts shift when strong acid or strong base is added. Adding acid converts AA^- to HAHA, while adding base converts HAHA to AA^-. The key takeaway is that the buffer’s pH responds to how these changes alter the ratio [A]/[HA][A^-]/[HA], not just the presence of the components. Source

  • A+H3O+HA+H2OA^- + H_3O^+ \rightarrow HA + H_2O

  • This decreases [A][A^-] and increases [HA][HA]

  • The ratio [A][HA]\frac{[A^-]}{[HA]} decreases, so pH falls

A more concentrated buffer has larger initial amounts of AA^- and HAHA, so the same added amount of H3O+H_3O^+ produces a smaller fractional change in the ratio, causing a smaller pH change.

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Comparison plot showing how pH responds to the same addition of strong base for buffers of different total concentrations. As concentration increases, the pH change per added increment becomes smaller, demonstrating greater buffer capacity even when the buffer ratio (and initial pH) are held constant. This is the graphical expression of “more inventory” of HAHA and AA^- resisting ratio change. Source

What happens when strong base is added

Added OHOH^- is consumed mostly by the weak acid:

  • HA+OHA+H2OHA + OH^- \rightarrow A^- + H_2O

  • This decreases [HA][HA] and increases [A][A^-]

  • The ratio [A][HA]\frac{[A^-]}{[HA]} increases, so pH rises

Again, when both components are more concentrated (but in the same ratio), the same added moles of OHOH^- change the ratio by a smaller percentage, so the pH is more stable.

What “constant ratio” really implies in practice

Same ratio → same pH (initially)

Two buffers with the same pKapK_a and the same [A][HA]\frac{[A^-]}{[HA]} will have essentially the same initial pH, even if one is 10× more concentrated.

Higher concentrations → greater resistance to pH change

At constant ratio, increasing concentration increases capacity because:

  • There are more moles of the conjugate pair available per litre

  • The neutralisation reactions can proceed further before the ratio is noticeably altered

  • The buffer can tolerate larger additions of strong acid/base before leaving its effective buffering region

Limits to the “same pH” claim

In AP Chemistry, the ratio model is the key idea. In real solutions, very high concentrations can introduce non-ideal effects (activities), but the syllabus-level takeaway remains: pH depends on ratio; capacity depends on concentration.

FAQ

Use a mole-based check: compare the moles of $HA$ and $A^-$ present to the moles of strong acid/base you plan to add.

A rough guideline: if added moles are a small fraction (for example, <5–10%) of the relevant buffer component, the pH change is typically small.

Ideally, no: dilution lowers both $[HA]$ and $[A^-]$ by the same factor, leaving $\frac{[A^-]}{[HA]}$ unchanged.

In very dilute buffers, water autoionisation and measurement limits can make deviations more noticeable.

Because pH depends on the ratio at a snapshot in time, but capacity is about how much reaction must occur before that ratio changes appreciably.

More concentration means more moles of each component to absorb added $H_3O^+$ or $OH^-$.

Capacity depends on total moles present, not just molarity.

  • Same molarity, larger volume $\rightarrow$ more total moles $\rightarrow$ higher total capacity

  • Same total moles, larger volume $\rightarrow$ lower molarity but similar total neutralisation ability

Non-ideal solution behaviour can matter: ion–ion interactions change effective concentrations (activities).

This can shift measured pH slightly even when analytical concentrations preserve $\frac{[A^-]}{[HA]}$.

Practice Questions

Q1 (2 marks) Two HA/AHA/A^- buffers have the same [A][HA]=1.0\frac{[A^-]}{[HA]}=1.0 at 2525^\circC. Buffer 1 is 0.100.10 M in each component; Buffer 2 is 1.01.0 M in each component. Compare (i) their initial pH and (ii) their buffer capacity.

  • Initial pH is the same for both because [A][HA]\frac{[A^-]}{[HA]} is the same (1)

  • Buffer 2 has greater capacity because both components are more concentrated (more moles available to neutralise added acid/base) (1)

Q2 (5 marks) A student prepares two buffers using the same conjugate pair HA/AHA/A^-. Buffer X contains 0.0200.020 mol HAHA and 0.0200.020 mol AA^-. Buffer Y contains 0.2000.200 mol HAHA and 0.2000.200 mol AA^-. Each buffer is made up to 1.001.00 L. Both are then challenged with 0.0100.010 mol of strong acid (H3O+H_3O^+). (a) State which buffer shows the smaller pH decrease. (1 mark) (b) Explain using the change in the ratio [A][HA]\frac{[A^-]}{[HA]}. (2 marks) (c) State whether the initial pH values of X and Y are the same or different, and why. (2 marks)

  • (a) Buffer Y (1)

  • (b) Adding H3O+H_3O^+ converts AA^- to HAHA; the ratio [A][HA]\frac{[A^-]}{[HA]} decreases (1)

  • (b) The same 0.0100.010 mol causes a smaller fractional (percentage) change in the ratio in Y because initial moles are larger (1)

  • (c) Same initial pH (1)

  • (c) Because both have the same [A][HA]\frac{[A^-]}{[HA]} (here, 1.0), so Henderson–Hasselbalch gives the same pH (1)

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