17.1 Buffers

Buffers and the Henderson-Hasselbalch Equation
General Chemistry 17.1
Buffers are solutions that resist changes in pH, composed of a weak acid paired with its conjugate base or a weak base paired with its conjugate acid. The Henderson-Hasselbalch equation—pH = pKa + log([A−]/[HA])—provides a streamlined method for calculating buffer pH without traditional ICE tables. This lesson covers buffer composition and capacity, the pKa ± 1 buffer range, polyprotic acid buffer systems, 3 methods for preparing buffers, and worked examples of pH calculations before and after adding strong acid.
What Is a Buffer in Chemistry?
A buffer is a solution that resists changes in pH when small amounts of strong acid or strong base are added. Why does that matter? Many chemical reactions are pH-sensitive—they only proceed favorably within a narrow pH range, so they are often carried out in a buffered environment.
More importantly, most living organisms survive only within a very narrow pH window. Your blood, for example, maintains a pH of approximately 7.4—just on the basic side of neutral. If that pH drops below 7.1 or climbs above 7.8 for any significant period of time, the consequences are fatal. Your blood is therefore heavily buffered against pH changes.
Composition of a Buffer: Weak Acid and Conjugate Base
A buffer maintains pH by virtue of what it contains. Every buffer is composed of a weak acid paired with its conjugate base, or equivalently, a weak base paired with its conjugate acid. The key word here is weak—a strong acid with its conjugate base does not form a buffer, nor does a strong base with its conjugate acid.
Example: Common Buffer Pairs in Chemistry
Weak acid + conjugate base: HF paired with F−
Weak base + conjugate acid: NH₃ paired with NH₄+
Using Salts to Supply the Conjugate Ion
When you need to add ions like F− or NH₄+ to a solution, you don't just grab a bottle of bare ions off the shelf. Instead, these are added as part of a salt, as covered in chapter 16.
For a fluoride buffer, you want a cation that won't influence the solution—a negligible cation. Group 1 metal salts (lithium, sodium, potassium, rubidium, cesium) fit the bill perfectly: they're both negligible and soluble with fluoride. Group 2 metal fluorides tend to be insoluble, so they're ruled out. Among the Group 1 options, sodium fluoride (NaF) is by far the most common choice.
For an ammonia buffer, you need a negligible anion paired with the ammonium cation. The best candidates are conjugate bases of strong acids. Chloride (Cl−) is the most common, making ammonium chloride (NH₄Cl) the standard choice. Ammonium bromide, ammonium iodide, ammonium chlorate, and ammonium nitrate would also work, but NH₄Cl is what you'll see most often.
Tip: When selecting a salt for your buffer, always choose ions that are negligible—meaning they won't hydrolyze or otherwise affect the pH. Group 1 metal cations and conjugate bases of strong acids are your safest bets.
Buffer Ratios and Maximum Buffering Capacity
To function as a buffer, the weak acid and conjugate base must be mixed in similar amounts—ideally equimolar, meaning equal moles. When the ratio is exactly one-to-one, the buffer achieves its maximum buffering capacity, providing the greatest resistance to pH changes.
However, a solution still functions as a buffer if there is up to 10 times more acid than conjugate base, or up to 10 times more conjugate base than acid. Beyond that 10-fold ratio, the solution loses its buffering ability and will no longer resist pH changes effectively.
How a Buffer Protects Against pH Change
What causes pH to change in the first place? Typically, the addition of a strong acid or base. Think of the buffer as protecting the water molecules in the solution.
In unbuffered water, adding an acid protonates water to form H₃O+, while adding a base deprotonates water to form OH−—both of which directly shift the pH. A buffer prevents this by offering better alternatives:
- If a base is added: The weak acid (HF) is a better proton donor than water, so it donates H+ to the base instead.
- If an acid is added: The conjugate base (F−) is a better proton acceptor than water, so it absorbs the H+ instead.
The net result? Instead of converting water into hydronium or hydroxide—which would dramatically shift the pH—the buffer simply adjusts the ratio of HF to NaF in the solution. That produces only a small change in pH rather than a large one.
Key Insight: A buffer works because it contains something that is a better acid than water and something that is a better base than water. Together, they shield the water molecules from being directly protonated or deprotonated.
pKa, Buffer Range, and the Logarithmic Scale
What Is pKa?
When working with buffers, you'll encounter pKa far more often than Ka. The pKa is simply the negative logarithm of the Ka:
Example: Calculating pKa for HF
Ka for HF = 6.8 × 10−4
pKa = −log(6.8 × 10−4) = 3.17 (often rounded to 3.2)
Buffer calculations are frequently more convenient using pKa values. You may be given the Ka and need to convert, or the pKa may be provided directly.
Buffer Range = pKa ± 1
When weak acid and conjugate base are present in an exact one-to-one ratio, the pH equals the pKa. Because the pH scale is logarithmic, shifting the ratio by a factor of 10 changes the pH by exactly one unit:
| Ratio (Acid : Conjugate Base) | pH Relative to pKa | pH for HF/NaF (pKa = 3.2) |
|---|---|---|
| 10 : 1 (10× more acid) | pKa − 1 | 2.2 |
| 1 : 1 (equimolar) | pKa | 3.2 |
| 1 : 10 (10× more base) | pKa + 1 | 4.2 |
The buffer range is therefore pKa ± 1. Within this window, the solution effectively resists pH changes—best at the pKa itself, but functional throughout the range. Outside this window, the solution can no longer buffer effectively.
Acetic Acid/Sodium Acetate Buffer Range Example
Example: Buffer Range for Acetic Acid
Acetic acid has a pKa of 4.8.
- Equimolar CH₃COOH and CH₃COONa → pH = 4.8
- 10× more acetic acid → pH = 3.8
- 10× more sodium acetate → pH = 5.8
Buffer range: 3.8 to 5.8 (pKa ± 1)
| Acid | pKa |
|---|---|
| HF | 3.2 |
| CH3COOH | 4.8 |
| H2CO3 | 6.4, 10.3 |
| H3PO4 | 2.1, 7.2, 12.4 |
Buffer Ranges for Polyprotic Acids
Polyprotic acids have more than one ionizable proton, which means they have multiple Ka values, multiple pKa values, and multiple buffer ranges. This makes them remarkably versatile for buffering at different pH targets.
Carbonic Acid: 2 Buffer Ranges
Carbonic acid (H₂CO₃) is diprotic, with two acidic protons to donate. Each deprotonation has its own pKa:
| Equilibrium | Acid/Base Pair | pKa | Buffer Range |
|---|---|---|---|
| First deprotonation | H₂CO₃ / HCO₃− | 6.4 | 5.4 – 7.4 |
| Second deprotonation | HCO₃− / CO₃²− | 10.3 | 9.3 – 11.3 |
Notice that each successive pKa is higher, reflecting the fact that removing additional protons becomes progressively more difficult. A lower Ka corresponds to a higher pKa, indicating a weaker acid.
Remember: For polyprotic acids, higher pKa = weaker acid = harder to remove the next proton. This is the opposite relationship you might initially expect when comparing Ka and pKa.
Phosphoric Acid: 3 pKa Values and Physiological Buffering
Phosphoric acid (H₃PO₄) has three acidic protons and therefore 3 pKa values: 2.1, 7.2, and 12.4. The second pKa at 7.2 is especially useful because it falls right near physiological pH, making phosphate buffers extremely common for biological experiments, cell cultures, and biochemistry applications.
Carbonic Acid and Blood Buffering
The first equilibrium of carbonic acid is a major component of your blood's buffering system. In the body, dissolved CO₂—the carbon dioxide you exhale—combines with water to form carbonic acid. That carbonic acid then participates in the equilibrium with bicarbonate:
Example: The Blood Buffer System
CO₂ + H₂O ↔ H₂CO₃ ↔ H+ + HCO₃−
This equilibrium continuously buffers your blood, keeping the pH stable near 7.4 so that you can keep on living.
3 Ways to Prepare a Buffer Solution
Creating a buffer isn't about what you add—it's about what you end up with. The goal is always the same: a solution containing a roughly one-to-one ratio of weak acid and its conjugate base. There are 3 ways to prepare a buffer solution.
Method 1: Mix Weak Acid Directly with Its Conjugate Base Salt
The most straightforward approach to buffer preparation: combine the weak acid and a salt of its conjugate base in approximately equal amounts.
Example: Mix HF with NaF in a ~1:1 ratio. You immediately have weak acid and conjugate base together—that's a buffer.
Method 2: Mix a Weak Acid with a Strong Base (2:1 Ratio)
Instead of adding the conjugate base directly, you can create it by partially neutralizing a weak acid with a strong base. The strong base converts some of the weak acid into its conjugate base. The trick is using a two-to-one ratio—two parts weak acid to one part strong base—so that exactly half the weak acid gets neutralized.
Example: HF + NaOH in a 2:1 Ratio
Start with 10 mol HF and add 5 mol NaOH:
HF + NaOH → NaF + H₂O
The NaOH is limiting, so all 5 mol are consumed. This uses up 5 mol of HF and produces 5 mol of NaF.
Result: 5 mol HF + 5 mol NaF = a 1:1 buffer.
Method 3: Mix a Weak Base with a Strong Acid (2:1 Ratio)
This works exactly like Method 2, but in reverse. Partially neutralize a weak base with a strong acid using a two-to-one ratio (two parts weak base to one part strong acid). Half the weak base gets converted into its conjugate acid, leaving a 1:1 mixture.
Example: Mix NaF (weak base) with HCl (strong acid) in a 2:1 ratio. Half the NaF gets neutralized to form HF, while the other half remains as NaF. Result: a 1:1 buffer of HF and NaF.
2 Common Wrong Answers to Watch For
Exam questions love to test whether you truly understand buffer composition. Watch out for these traps:
Common Mistake 1: A strong acid with its conjugate base is not a buffer. The conjugate base of a strong acid is a negligible base—you just end up with a very acidic solution. It must be a weak acid with its conjugate base.
Common Mistake 2: Mixing a weak acid with a strong base in a 1:1 ratio does not produce a buffer. Equal amounts of strong base will neutralize all the weak acid, leaving only the conjugate base in solution. You must use a 2:1 ratio (two parts weak, one part strong) to preserve half the weak acid.
| 3 Ways to Prepare a Buffer |
|---|
| Weak Acid / Conjugate Base 1 : 1 |
| Weak Acid / Strong Base 2 : 1 |
| Weak Base / Strong Acid 2 : 1 |
Buffer pH Calculations: The Henderson-Hasselbalch Equation
Why Use the Henderson-Hasselbalch Equation?
Calculating the pH of a buffer is the fifth type of pH calculation you'll encounter in general chemistry, following strong acid, strong base, weak acid, and weak base calculations from previous chapters. For buffers, the Henderson-Hasselbalch equation provides a more convenient approach than traditional ICE tables.
This equation applies only when both a weak acid and its conjugate base are present in solution. If either one is missing (concentration of zero), the equation breaks down—you'd be taking the log of zero, which is undefined.
Note: You could technically use the Ka expression or the Kb expression instead, since Henderson-Hasselbalch is derived from Ka. But for buffer problems, Henderson-Hasselbalch is simply more efficient.
Deriving the Henderson-Hasselbalch Equation
Starting from the Ka expression and taking the negative logarithm of both sides:
- Begin with: Ka = [H+][A−] / [HA]
- Take the log of both sides: log(Ka) = log([H+]) + log([A−]/[HA])
- Multiply through by −1: −log(Ka) = −log([H+]) − log([A−]/[HA])
- Recognize that −log(Ka) = pKa and −log([H+]) = pH
- Rearrange to arrive at the final form:
The Henderson-Hasselbalch Equation:
pH = pKa + log([A−] / [HA])
4 Versions of the Equation (and Which One to Use)
There are actually 4 versions of this equation floating around, which can be a source of confusion. Since log(x/y) = −log(y/x), you can flip the ratio and change the sign. Additionally, there are pOH/pKb versions. To keep things simple, stick with this one form:
pH = pKa + log([A−] / [HA])
This is the most commonly presented version, and any buffer pH calculation works exactly the same way using this form alone.
Worked Example: Finding the pH of a Buffer Solution

Problem: What is the pH of a solution containing 0.10 M CH₃COOH (acetic acid) and 0.080 M CH₃COONa (sodium acetate)? The Ka of acetic acid is 1.76 × 10−5.
First, recognize that this is a buffer: you have a weak acid and its conjugate base present together in similar amounts. With a buffer, any ±x terms in an ICE table would be negligible, so skip the ICE table entirely and go straight to Henderson-Hasselbalch.
Step 1: Convert Ka to pKa:
pKa = −log(1.76 × 10−5) = 4.75
Step 2: Apply the Henderson-Hasselbalch equation:
pH = 4.75 + log(0.080 / 0.10) = 4.75 + log(0.80) = 4.75 + (−0.10) = 4.65
Sanity Check: There is slightly more acid than conjugate base, so the pH should be slightly below the pKa of 4.75. Indeed, 4.65 < 4.75. If the ratio were exactly 1:1, log(1) = 0 and pH would equal exactly the pKa—confirming the rule that pH = pKa at a one-to-one ratio.
Worked Example: pH After Adding a Strong Acid to a Buffer
Setting Up the Problem
Problem: What would be the pH if 5.0 mL of 0.10 M HCl were added to 100 mL of the buffer solution from the previous example (pH = 4.65)?
Because this is a buffer, the pH should change only slightly. We expect it to decrease a little (we're adding acid), but not by much.
Neutralization Reaction First
When HCl (a strong acid) enters the buffer, it neutralizes the conjugate base. Strong acids neutralize all bases—strong, weak, everything. The base in this solution is the acetate ion (CH₃COO−):
HCl + CH₃COO− → CH₃COOH + Cl−
This reaction goes to completion because HCl fully dissociates. A reaction that goes to completion requires a limiting reagent calculation, which means we need moles, not molarities.
Converting to Moles
Using moles = molarity × volume (in liters):
- Conjugate base (CH₃COO−): 0.100 L × 0.080 mol/L = 0.0080 mol
- Conjugate acid (CH₃COOH): 0.100 L × 0.10 mol/L = 0.010 mol
- HCl added: 0.0050 L × 0.10 mol/L = 0.00050 mol
Limiting Reagent Stoichiometry
The HCl is the limiting reagent (0.00050 mol). It reacts in a 1:1 ratio with the conjugate base, consuming 0.00050 mol of acetate while producing 0.00050 mol of acetic acid:
- Conjugate base remaining: 0.0080 − 0.00050 = 0.0075 mol
- HCl remaining: 0 mol (completely consumed)
- Conjugate acid total: 0.010 + 0.00050 = 0.0105 mol
Both weak acid and conjugate base are still present in reasonable amounts, so the solution is still a buffer and Henderson-Hasselbalch still applies.
Why You Can Use Moles Instead of Molarities in Henderson-Hasselbalch
Here's a useful shortcut. In Henderson-Hasselbalch, the ratio [A−]/[HA] can be written as (moles of A− / V) / (moles of HA / V), where V is the total solution volume. Since V appears in both numerator and denominator, it cancels:
pH = pKa + log(moles of A− / moles of HA)
Important: You can't substitute moles for molarity just anywhere—it only works here because the Henderson-Hasselbalch equation uses a ratio of concentrations in the same solution, so the volume cancels.
Final pH Calculation
pH = 4.75 + log(0.0075 / 0.0105) = 4.75 + log(0.714) = 4.75 + (−0.15) = 4.60
The pH dropped from 4.65 to 4.60—a change of only 0.05 units. That's the buffer doing its job. For comparison, adding the same amount of HCl to 100 mL of pure water would have dropped the pH by several units.
The Pattern: What to Add or Subtract
Once you set up Henderson-Hasselbalch in terms of moles, the pattern is simple:
| What Was Added? | Numerator (A−) | Denominator (HA) | pH Change |
|---|---|---|---|
| Strong acid | Subtract (base consumed) | Add (acid formed) | Decreases |
| Strong base | Add (base formed) | Subtract (acid consumed) | Increases |
Common Mistake: Many students remember to subtract from whichever species gets neutralized, but they forget that the neutralization produces the conjugate partner. If strong acid neutralizes the base, don't just subtract from A−—also add to HA. Both changes matter.
8 Key Takeaways: Buffers and Henderson-Hasselbalch
- A buffer is a solution that resists changes in pH, composed of a weak acid paired with its conjugate base (or a weak base with its conjugate acid)—never a strong acid/base pair.
- A buffer achieves maximum buffering capacity at an equimolar ratio of weak acid and conjugate base. It still functions as a buffer up to a 10-fold excess of either component.
- The buffer range is pKa ± 1. At a 1:1 ratio, pH = pKa; a 10-fold change in ratio shifts pH by exactly one unit.
- Polyprotic acids have multiple pKa values and multiple buffer ranges, making them versatile for buffering at different pH values.
- There are 3 ways to prepare a buffer: mix weak acid with conjugate base salt directly, mix weak acid with strong base (2:1), or mix weak base with strong acid (2:1).
- The Henderson-Hasselbalch equation—pH = pKa + log([A−]/[HA])—is the standard tool for buffer pH calculations.
- When strong acid or base is added to a buffer, perform the neutralization stoichiometry first (in moles), then apply Henderson-Hasselbalch to the remaining amounts.
- You can use moles instead of molarities in Henderson-Hasselbalch because the ratio of concentrations in the same solution causes the volume to cancel.

