Calculate the pH of 0.085 M Pyridinium Bromide
Use this premium chemistry calculator to estimate the pH of an aqueous pyridinium bromide solution using the weak acid dissociation of the pyridinium ion, the conjugate acid of pyridine. The default values are prefilled for a 0.085 M sample.
Pyridinium ion: C5H5NH+ ⇌ H+ + C5H5N
Ka = 10-pKa
For initial concentration C, solve x from x2 / (C – x) = Ka, where x = [H+].
pH = -log10[H+]
How to calculate the pH of 0.085 M pyridinium bromide
Pyridinium bromide is the salt formed when pyridine accepts a proton and pairs with bromide as the counterion. In water, the bromide ion is essentially a spectator ion because it is the conjugate base of the strong acid HBr and has negligible basicity in normal aqueous conditions. The chemistry that matters for pH comes from the pyridinium ion, C5H5NH+, which behaves as a weak acid. That means a solution of pyridinium bromide will be acidic, but not strongly acidic.
To calculate the pH of a 0.085 M pyridinium bromide solution, you treat the salt as a source of 0.085 M pyridinium ion and write its acid dissociation equilibrium:
C5H5NH+ + H2O ⇌ H3O+ + C5H5N
The equilibrium constant is the acid dissociation constant Ka. If the pKa of pyridinium is 5.25, then:
Ka = 10-5.25 ≈ 5.62 × 10-6
Let the initial concentration of pyridinium ion be C = 0.085 M. If x dissociates, then at equilibrium:
- [H+] = x
- [C5H5N] = x
- [C5H5NH+] = 0.085 – x
Substitute these into the weak acid expression:
Ka = x2 / (0.085 – x)
For many weak acids, an excellent first estimate is the shortcut x ≈ √(KaC). Using that approximation:
x ≈ √((5.62 × 10-6)(0.085)) ≈ 6.91 × 10-4 M
Then the pH is:
pH = -log(6.91 × 10-4) ≈ 3.16
If you solve the quadratic exactly, the answer remains essentially the same because x is much smaller than the initial 0.085 M concentration. The exact result is about pH = 3.16. So the pH of 0.085 M pyridinium bromide is approximately 3.16, assuming a pyridinium pKa near 5.25 at room temperature.
Why pyridinium bromide is acidic
Pyridine itself is a weak base. When pyridine is protonated, it becomes pyridinium, which is the conjugate acid of that weak base. Conjugate acids of weak bases donate protons to water to some extent, producing hydronium ions and lowering pH. This is why salts like pyridinium bromide, ammonium chloride, and anilinium salts often give acidic solutions.
The bromide ion does not significantly hydrolyze water, so it does not counteract the acidity. The practical rule is simple: a salt made from a weak base and a strong acid generally gives an acidic solution.
Quick acid-base classification
- Pyridine: weak base
- Pyridinium ion: weak acid
- HBr: strong acid
- Br–: negligible basicity in water
- Pyridinium bromide: acidic salt
Step by step method for students
- Identify the acid-base active ion in the salt. For pyridinium bromide, it is pyridinium.
- Write the acid dissociation reaction of pyridinium in water.
- Use the pKa of pyridinium to calculate Ka.
- Set up an ICE table with initial concentration 0.085 M.
- Write the equilibrium expression Ka = x2 / (0.085 – x).
- Solve either by the weak acid approximation or by the quadratic formula.
- Convert x to pH using pH = -log[H+].
- Check that x is less than 5 percent of the initial concentration if you used the approximation.
5 percent rule check
Using the approximate value x = 6.91 × 10-4 M:
(x / 0.085) × 100 ≈ 0.81%
Because 0.81 percent is well below 5 percent, the approximation is valid. That means the shortcut and the exact quadratic method agree closely.
Exact calculation details
If you want the mathematically exact result, start from:
x2 + Kax – KaC = 0
Substitute Ka = 5.62 × 10-6 and C = 0.085:
x2 + (5.62 × 10-6)x – (4.78 × 10-7) = 0
Using the positive root:
x = [-Ka + √(Ka2 + 4KaC)] / 2
This gives x ≈ 6.88 × 10-4 M, so:
pH ≈ 3.16
Comparison data table: exact vs approximation
| Method | Assumed Ka | [H+] (M) | pH | Difference from exact |
|---|---|---|---|---|
| Exact quadratic | 5.62 × 10-6 | 6.88 × 10-4 | 3.162 | 0.000 pH units |
| Weak acid approximation | 5.62 × 10-6 | 6.91 × 10-4 | 3.160 | 0.002 pH units |
The difference is so small that for most general chemistry work, the approximation is completely acceptable. However, if you are writing a lab report, using software, or comparing with measured electrode data, the exact method is preferable.
How concentration changes the pH
The pH of a weak acid solution depends on both the acid strength and the formal concentration. If the pKa remains constant, increasing the concentration of pyridinium bromide increases the hydronium ion concentration and lowers the pH. Because the acid is weak, the change in pH is not linear with concentration. It follows the equilibrium relationship, and rough changes often track with the square root of concentration in the approximation regime.
| Pyridinium bromide concentration (M) | Approx. [H+] (M) | Approx. pH | Percent dissociation |
|---|---|---|---|
| 0.010 | 2.37 × 10-4 | 3.63 | 2.37% |
| 0.050 | 5.30 × 10-4 | 3.28 | 1.06% |
| 0.085 | 6.91 × 10-4 | 3.16 | 0.81% |
| 0.100 | 7.50 × 10-4 | 3.12 | 0.75% |
| 0.500 | 1.68 × 10-3 | 2.78 | 0.34% |
Notice two important trends in the table. First, larger concentration gives lower pH. Second, percent dissociation decreases as concentration rises, which is a characteristic behavior of weak electrolytes. At lower concentration, a larger fraction dissociates even if the absolute hydronium concentration is smaller.
Common mistakes when solving this problem
- Treating pyridinium bromide as a strong acid. It is not. Only the pyridinium ion acts as a weak acid.
- Using Kb for pyridine directly without converting. If you start with Kb, use Ka = Kw / Kb.
- Forgetting that bromide is a spectator ion. Br– does not appreciably affect pH here.
- Using pKa and Ka interchangeably. You must convert pKa to Ka before substituting into the equilibrium expression.
- Missing the log sign convention. pH = -log[H+], so a larger hydronium concentration means a smaller pH value.
Alternative route using Kb of pyridine
Some textbooks list the basicity of pyridine rather than the acidity of pyridinium. If pyridine has Kb around 1.7 × 10-9 at 25 C, then:
Ka(pyridinium) = Kw / Kb = (1.0 × 10-14) / (1.7 × 10-9) ≈ 5.9 × 10-6
This value is very close to the earlier Ka derived from pKa = 5.25, and it leads to nearly the same pH. Small differences in tabulated constants can shift the answer by a few hundredths of a pH unit, which is normal in acid-base chemistry.
Real world interpretation of the result
A pH near 3.16 means the solution is clearly acidic, but much less acidic than a strong acid solution of the same formal concentration. For comparison, a 0.085 M strong monoprotic acid would have pH near 1.07, assuming complete dissociation. Pyridinium bromide is therefore acidic because of hydrolysis, but its weak acid character limits hydronium production.
This distinction matters in synthesis, analytical chemistry, and buffer preparation. Pyridinium salts often appear in organic and biochemical settings, where proton transfer equilibria influence reaction rates, extraction behavior, and the protonation state of nitrogen-containing heterocycles.
Authoritative references for equilibrium constants and acid-base fundamentals
- National Institute of Standards and Technology (NIST)
- LibreTexts Chemistry, hosted by educational institutions
- United States Environmental Protection Agency (EPA)
Final answer
If you assume pKa = 5.25 for the pyridinium ion, then the pH of 0.085 M pyridinium bromide is approximately 3.16. The exact quadratic and the common weak acid approximation both support that result. In most classroom and laboratory contexts, reporting the pH as 3.16 is appropriate.