Calculate the pH of 0.142 M Maleic Acid
Use this premium diprotic acid calculator to estimate the pH of a maleic acid solution using either an exact diprotic equilibrium model or a first-dissociation approximation. Default values are set for 0.142 M maleic acid at 25 degrees Celsius with commonly cited acid dissociation constants.
Results
Click Calculate pH to compute the pH of 0.142 M maleic acid and view species distribution.
Expert Guide: How to Calculate the pH of 0.142 M Maleic Acid
Calculating the pH of 0.142 M maleic acid is a classic acid-base equilibrium problem because maleic acid is not a simple monoprotic acid. It is a diprotic acid, meaning each molecule can donate two protons in water. The chemical formula is often written as H2A, where the first ionization produces HA– and the second ionization produces A2-. In practical classroom and lab work, the first dissociation dominates the pH because maleic acid has a relatively strong first acid dissociation compared with its much weaker second dissociation.
For a 0.142 M solution, the expected pH is strongly acidic, typically close to 1.41 when using common 25 degrees Celsius constants such as Ka1 = 1.48 × 10-2 and Ka2 = 2.60 × 10-7. The exact answer varies slightly depending on which literature constants you choose, the ionic strength of the solution, and whether your source tabulates thermodynamic or concentration-based values. That is why a good calculator should let you adjust Ka values while still providing realistic defaults.
Why maleic acid needs a diprotic treatment
Maleic acid dissociates in two steps:
- H2A ⇌ H+ + HA–
- HA– ⇌ H+ + A2-
Each step has its own acid dissociation constant. The first constant, Ka1, is much larger than Ka2. That means the first proton is released much more readily than the second. In numerical terms, maleic acid is strong enough in its first dissociation that the pH ends up well below 2 for a 0.142 M solution, but the second proton remains mostly attached because the surrounding solution is already acidic and suppresses further ionization.
| Property | Typical value | Why it matters |
|---|---|---|
| Formula | C4H4O4 | Identifies maleic acid as a dicarboxylic acid with two ionizable protons. |
| Molar mass | 116.07 g/mol | Useful when preparing a 0.142 M solution from a weighed mass. |
| Ka1 at 25 degrees Celsius | 1.48 × 10-2 | Controls the major source of H+ in solution. |
| Ka2 at 25 degrees Celsius | 2.60 × 10-7 | Usually contributes only slightly at this concentration. |
| pKa1 | 1.83 | Shows the first proton is released relatively easily. |
| pKa2 | 6.59 | Shows the second proton is much less acidic. |
Step-by-step calculation using the first dissociation approximation
The fastest hand calculation treats only the first dissociation as important:
H2A ⇌ H+ + HA–
Start with an initial concentration of 0.142 M maleic acid. Let x be the amount that dissociates in the first step.
- [H2A] = 0.142 – x
- [H+] = x
- [HA–] = x
Apply the Ka1 expression:
Ka1 = x2 / (0.142 – x)
Using Ka1 = 0.0148:
0.0148 = x2 / (0.142 – x)
Rearranging gives:
x2 + 0.0148x – 0.0021016 = 0
Solving the quadratic gives x ≈ 0.0390 M. Therefore:
pH = -log[H+] = -log(0.0390) ≈ 1.41
This is already an excellent estimate. Because Ka2 is so much smaller than Ka1, the second ionization adds only a very small amount of extra H+.
Exact diprotic method and why it is more rigorous
The exact method uses all relevant equilibria together. Instead of assuming only one proton matters, it accounts for H2A, HA–, A2-, H+, and the water autoionization term. A compact way to solve this is with a charge-balance equation plus alpha fractions for the three acid species. For a diprotic acid:
- α0 = [H+]2 / D
- α1 = Ka1[H+] / D
- α2 = Ka1Ka2 / D
- D = [H+]2 + Ka1[H+] + Ka1Ka2
Then the species concentrations are:
- [H2A] = Cα0
- [HA–] = Cα1
- [A2-] = Cα2
The charge balance becomes:
[H+] = [OH–] + [HA–] + 2[A2-]
Since [OH–] is tiny in a strongly acidic solution, the answer lands very close to the first-dissociation estimate. In this particular case, the exact model confirms that the final pH remains about 1.41.
What the 0.142 M concentration tells you
Concentration matters enormously. A more dilute maleic acid solution would have a higher pH because there are fewer acid molecules available per liter to generate hydrogen ions. At 0.142 M, the acid is concentrated enough that the first dissociation produces a substantial H+ concentration. Because pH is logarithmic, even modest changes in hydrogen ion concentration shift the pH noticeably.
| Scenario | Input concentration | Approximate pH using Ka1 = 1.48 × 10-2 | Interpretation |
|---|---|---|---|
| Dilute maleic acid | 0.010 M | 2.08 | Acidic, but much less acidic than the 0.142 M case. |
| Target problem | 0.142 M | 1.41 | Strongly acidic because first dissociation generates significant H+. |
| More concentrated sample | 0.500 M | 1.09 | Lower pH because the available acid concentration is much higher. |
Common mistakes students make
- Assuming maleic acid is monoprotic and forgetting the second dissociation exists.
- Assuming both protons dissociate fully like a strong acid. They do not.
- Using pKa values from a different temperature or ionic strength without noting the difference.
- Dropping the quadratic too early. Here, the percent dissociation is large enough that the small-x approximation is not appropriate.
- Confusing maleic acid with fumaric acid, which has different acid dissociation behavior.
Why the second dissociation is small here
Once the first dissociation has produced about 0.039 M hydrogen ions, the solution is already strongly acidic. That large existing [H+] pushes the second equilibrium to the left, suppressing conversion of HA– into A2-. In other words, the common-ion effect works against the second proton being released. This is why a first-step calculation gets so close to the exact result.
Practical interpretation of the result
A pH near 1.41 means the solution is significantly acidic and should be handled with appropriate lab safety practices. While maleic acid is a weak acid in the formal equilibrium sense, a 0.142 M solution still has a hydrogen ion concentration near 4 × 10-2 M, which is substantial. In experiments involving titration, buffer design, or organic acid comparison, maleic acid often appears stronger in its first dissociation than many students expect.
Recommended authoritative references
If you want to verify acid constants, pH concepts, or polyprotic acid methods, these sources are excellent starting points:
- NIST Chemistry WebBook for critically evaluated chemical data and reference values.
- U.S. EPA overview of pH for a clear explanation of acidity and the pH scale.
- Purdue University overview of polyprotic acids for the equilibrium framework used in problems like this.
Final takeaway
To calculate the pH of 0.142 M maleic acid, the most reliable quick approach is to solve the first dissociation equilibrium with a quadratic equation using Ka1. That yields a pH of about 1.41. If you apply a full diprotic equilibrium treatment, the answer changes very little because Ka2 is tiny compared with Ka1 and the solution is already strongly acidic after the first ionization step. In short, the chemistry is diprotic, but the pH is controlled mostly by the first proton.
The calculator above automates both methods, formats the key values, and displays a chart of species concentrations so you can see exactly how the acid is distributed in solution. That combination of numerical result and visual interpretation is the best way to understand why 0.142 M maleic acid has a pH near 1.41.