pKa Calculator
Convert between Ka and pKa values or solve the Henderson-Hasselbalch equation. Select a mode below, enter your values, and get instant results with step-by-step calculations.
Acid Dissociation Equilibrium
1. What is pKa?
The pKa value is a quantitative measure of how strong an acid is in solution. Formally, it is the negative base-10 logarithm of the acid dissociation constant (Ka):
A lower pKa indicates a stronger acid -- meaning the acid donates protons more readily. Conversely, a higher pKa indicates a weaker acid that holds on to its proton more tightly. The pKa scale is logarithmic: each unit change in pKa corresponds to a tenfold change in acid strength.
- Strong acids (e.g., HCl, H2SO4) have very low or even negative pKa values.
- Weak acids (e.g., acetic acid, carbonic acid) have pKa values typically between 2 and 14.
- Very weak acids (e.g., water, ethanol) have pKa values above 14.
2. What is Ka?
Ka stands for the acid dissociation constant. It describes the equilibrium position for the dissociation of an acid in water. For a generic acid HA dissolving in water:
The equilibrium expression is:
Where the square brackets denote molar concentrations at equilibrium. A large Ka value means the equilibrium lies far to the right (strong acid, extensive dissociation). A small Ka value means the equilibrium favors the undissociated acid (weak acid).
Because Ka values for weak acids are often very small numbers expressed in scientific notation (e.g., 1.8 × 10−5), chemists find it more convenient to work with pKa values, which compress the wide range of Ka into a more manageable numerical scale.
3. The pKa Formula
The fundamental relationship between pKa and Ka is:
And conversely:
These two expressions are inverse operations. If you know Ka, you can find pKa by taking the negative logarithm. If you know pKa, you can find Ka by raising 10 to the negative power of pKa.
pKa = −log10(1.8 × 10−5) = −(−4.74) = 4.74
4. pKa vs pH: How They Differ and Relate
While pKa and pH both use the "p" notation (negative logarithm), they measure fundamentally different things:
- pH measures the hydrogen ion concentration in a solution: pH = −log10[H+]. It tells you how acidic or basic a specific solution is.
- pKa is a property of the acid itself. It tells you how strong an acid is and does not change with concentration (at a given temperature).
The critical connection between pKa and pH arises when an acid is in solution:
- When pH = pKa, the acid is exactly 50% dissociated -- equal concentrations of HA and A− exist.
- When pH < pKa, the protonated form (HA) dominates.
- When pH > pKa, the deprotonated form (A−) dominates.
This relationship is central to buffer chemistry and is formalized in the Henderson-Hasselbalch equation.
5. The Henderson-Hasselbalch Equation
The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of an acid and the ratio of the concentrations of the conjugate base and the acid:
Derivation
Starting from the Ka expression:
Rearrange to isolate [H+]:
Take the negative log of both sides:
Since −log[H+] = pH and −log(Ka) = pKa, and using the log identity −log(a/b) = log(b/a):
Key Insights
- When [A−] = [HA], the log term equals zero, so pH = pKa.
- For every 10-fold increase in the [A−]/[HA] ratio, pH increases by 1 unit.
- Effective buffer range is typically pKa ± 1, where the buffer can resist pH changes.
- The equation assumes ideal dilute solutions and that the Ka is not too large (works best for weak acids).
6. How to Calculate pKa Step by Step
Method 1: From Ka Value
Step 1: Write the formula: pKa = −log10(Ka)
Step 2: Substitute: pKa = −log10(1.8 × 10−4)
Step 3: Calculate: log10(1.8 × 10−4) = log(1.8) + log(10−4) = 0.2553 + (−4) = −3.745
Step 4: Take the negative: pKa = −(−3.745) = 3.74
Method 2: From Experimental pH and Concentration Data
Step 1: Use Henderson-Hasselbalch: pH = pKa + log([A−]/[HA])
Step 2: Rearrange: pKa = pH − log([A−]/[HA])
Step 3: Substitute: pKa = 4.62 − log(0.15/0.20) = 4.62 − log(0.75)
Step 4: Calculate: pKa = 4.62 − (−0.125) = 4.74
Method 3: From pKa to Ka
Step 1: Write the formula: Ka = 10−pKa
Step 2: Substitute: Ka = 10−6.37
Step 3: Calculate: Ka = 4.27 × 10−7
7. pKa Table of Common Acids
Below is a reference table of Ka and pKa values for common acids at 25 °C. Strong acids are shown in red and weak acids in blue.
| Acid | Formula | Ka | pKa | Strength |
|---|---|---|---|---|
| Hydroiodic acid | HI | ~1010 | −10 | Strong |
| Hydrobromic acid | HBr | ~109 | −9 | Strong |
| Hydrochloric acid | HCl | ~106 | −6 | Strong |
| Sulfuric acid (1st H) | H2SO4 | ~103 | −3 | Strong |
| Nitric acid | HNO3 | ~24 | −1.38 | Strong |
| Sulfuric acid (2nd H) | HSO4− | 1.2 × 10−2 | 1.92 | Weak |
| Phosphoric acid (1st H) | H3PO4 | 7.5 × 10−3 | 2.12 | Weak |
| Hydrofluoric acid | HF | 6.8 × 10−4 | 3.17 | Weak |
| Nitrous acid | HNO2 | 4.5 × 10−4 | 3.35 | Weak |
| Formic acid | HCOOH | 1.8 × 10−4 | 3.74 | Weak |
| Benzoic acid | C6H5COOH | 6.3 × 10−5 | 4.20 | Weak |
| Acetic acid | CH3COOH | 1.8 × 10−5 | 4.74 | Weak |
| Carbonic acid (1st H) | H2CO3 | 4.3 × 10−7 | 6.37 | Weak |
| Hydrogen sulfide (1st H) | H2S | 1.0 × 10−7 | 7.00 | Weak |
| Hypochlorous acid | HClO | 2.9 × 10−8 | 7.54 | Weak |
| Ammonium ion | NH4+ | 5.6 × 10−10 | 9.25 | Weak |
| Hydrogen cyanide | HCN | 6.2 × 10−10 | 9.21 | Weak |
| Carbonic acid (2nd H) | HCO3− | 4.8 × 10−11 | 10.32 | Weak |
| Phosphoric acid (3rd H) | HPO42− | 4.2 × 10−13 | 12.38 | Weak |
| Water | H2O | 1.0 × 10−14 | 14.00 | Very Weak |
8. Strong Acids vs Weak Acids (pKa Perspective)
The distinction between strong and weak acids is one of the most fundamental concepts in chemistry, and pKa provides a precise way to quantify it.
Strong Acids
- Have pKa < −1 (typically much lower).
- Dissociate completely in water -- essentially 100% of the acid molecules release their protons.
- Examples: HCl (pKa = −6), HBr (pKa = −9), HNO3 (pKa = −1.38).
- Ka values are extremely large (often > 1), meaning the equilibrium overwhelmingly favors products.
Weak Acids
- Have pKa > −1 (most common weak acids have pKa between 2 and 14).
- Only partially dissociate in water -- an equilibrium exists between HA and its ions.
- Examples: acetic acid (pKa = 4.74), carbonic acid (pKa = 6.37), ammonium (pKa = 9.25).
- Ka values are small (typically 10−2 to 10−14).
The practical consequence is that strong acids lower the pH of solutions much more effectively per mole than weak acids. Additionally, weak acids can form buffer solutions when combined with their conjugate bases, while strong acids cannot (since they fully dissociate).
9. pKa and Buffer Solutions
A buffer solution resists changes in pH when small amounts of acid or base are added. Buffers consist of a weak acid and its conjugate base (or a weak base and its conjugate acid). The pKa of the acid is central to buffer design.
Buffer Capacity and pKa
- A buffer works most effectively when pH is within ±1 unit of the pKa of the weak acid component.
- Maximum buffer capacity occurs when pH = pKa, where [HA] = [A−].
- Beyond the pKa ± 1 range, the buffer capacity drops significantly because one form (HA or A−) overwhelmingly dominates.
Choosing the Right Buffer
To prepare a buffer at a target pH, choose an acid whose pKa is as close as possible to the desired pH. For example:
- pH 3.7 buffer: Use formic acid (pKa = 3.74) and sodium formate.
- pH 4.7 buffer: Use acetic acid (pKa = 4.74) and sodium acetate.
- pH 6.4 buffer: Use carbonic acid (pKa = 6.37) and sodium bicarbonate.
- pH 7.2 buffer: Use phosphoric acid/dihydrogen phosphate (pKa2 = 7.20) and sodium hydrogen phosphate.
- pH 9.2 buffer: Use ammonium (pKa = 9.25) and ammonia.
The Henderson-Hasselbalch equation is used to calculate the exact ratio of conjugate base to acid needed to achieve a specific pH within the effective buffer range.
10. Frequently Asked Questions
pKa measures acid strength (how readily a substance donates a proton), while pKb measures base strength (how readily a substance accepts a proton). They are related by the equation: pKa + pKb = 14 (at 25 °C in water). If you know the pKa of a conjugate acid, you can find the pKb of its conjugate base, and vice versa.
Yes. Strong acids have negative pKa values because their Ka values are greater than 1. For example, hydrochloric acid (HCl) has a pKa of approximately −6, meaning it dissociates essentially completely in water. A negative pKa simply indicates a very strong acid.
Yes. pKa values are temperature-dependent because Ka is an equilibrium constant, and equilibrium constants change with temperature according to the van 't Hoff equation. Most commonly cited pKa values are measured at 25 °C (298 K). For precise work, especially in biological systems (37 °C) or industrial processes, temperature corrections should be applied.
pKa is critical in pharmacology because it determines whether a drug molecule is ionized or un-ionized at physiological pH. Only the un-ionized form can typically cross cell membranes by passive diffusion. The proportion of ionized vs. un-ionized drug at a given pH is calculated using the Henderson-Hasselbalch equation. This directly affects drug absorption, distribution, and bioavailability.
pKa is most commonly determined by potentiometric titration, where the acid is titrated with a strong base while monitoring pH. At the half-equivalence point (where half the acid has been neutralized), pH = pKa. Other methods include UV-vis spectrophotometry (tracking absorbance changes with pH), NMR spectroscopy (observing chemical shift changes), and capillary electrophoresis.
A polyprotic acid can donate more than one proton. Each proton has its own Ka and pKa value. For example, phosphoric acid (H3PO4) has three dissociation steps: pKa1 = 2.12, pKa2 = 7.20, and pKa3 = 12.38. Each successive pKa is always larger than the previous one because it becomes progressively harder to remove a proton from an increasingly negatively charged species.
The Henderson-Hasselbalch equation is designed for weak acid/conjugate base buffer systems and generally should not be applied to strong acids. Since strong acids dissociate completely, there is no meaningful equilibrium between HA and A−, and the equation's assumptions break down. For strong acid pH calculations, simply use [H+] directly from the concentration of the fully dissociated acid.