Calculate the pH of a 3.0×10-8 M Solution of HBr
This premium calculator correctly handles very dilute strong acid solutions by including water autoionization, so you get the chemically accurate pH instead of the oversimplified classroom shortcut.
HBr pH Calculator
Why this problem is tricky
For concentrated strong acids, many students use pH = -log[H+], where [H+] is just the acid concentration. That shortcut fails when the acid concentration is close to 1.0×10^-7 M because pure water itself already contributes hydrogen ions through autoionization.
- Naive approach: [H+] = 3.0×10^-8 M gives pH about 7.52, which incorrectly suggests a basic or nearly neutral result.
- Correct approach: solve for total [H+] using both the acid and water equilibrium.
- At 25 C, Kw = 1.0×10^-14, so the proper equation becomes H^2 – C H – Kw = 0.
Expert Guide: How to Calculate the pH of a 3.0×10-8 M Solution of HBr
To calculate the pH of a 3.0×10^-8 M solution of HBr, you have to be more careful than you would be with a typical strong-acid problem. Hydrobromic acid is a strong acid, so in ordinary textbook conditions we usually assume it dissociates completely and contributes a hydrogen ion concentration equal to its formal molarity. If the concentration were something like 1.0×10^-2 M or 1.0×10^-3 M, that quick approach would work very well. However, at 3.0×10^-8 M, the acid concentration is smaller than the 1.0×10^-7 M hydrogen ion concentration associated with pure water at 25 C. That means water autoionization cannot be ignored.
This is exactly why this calculation appears in chemistry classes, exam prep materials, and tutoring sessions. It tests whether you understand not just the definition of pH, but also the limitations of approximations. In a very dilute strong acid solution, the total hydrogen ion concentration comes from two sources: the dissolved acid and water itself. If you overlook the water contribution, your answer will be wrong by a wide margin.
Step 1: Recognize that HBr is a strong acid
HBr is classified as a strong acid in water. That means it dissociates essentially completely:
Under normal circumstances, we often write:
For a 3.0×10^-8 M HBr solution, that shortcut would give:
That answer is not acceptable for this problem. A solution containing a strong acid should not come out with a pH above 7 under these assumptions. The contradiction tells you the simple approximation has broken down.
Step 2: Include the autoionization of water
At 25 C, water self-ionizes according to:
The equilibrium expression is:
In pure water at 25 C, this leads to:
Because the given HBr concentration is only 3.0×10^-8 M, it is of the same order of magnitude as the hydrogen ion concentration generated by water. So the total [H+] is not simply 3.0×10^-8 M. Instead, we must solve the equilibrium relationship together with charge balance.
Step 3: Set up the correct equation
Let the formal concentration of HBr be C = 3.0×10^-8 M. Since HBr is a strong acid, it contributes bromide ions at the same concentration, so:
Charge balance requires:
From water equilibrium:
Substitute that into the charge balance:
Multiply through by [H+]:
Rearrange into quadratic form:
Now use the quadratic formula:
We use the positive root because concentration must be positive.
Step 4: Plug in the numbers
Insert the values:
Compute the terms:
Then:
Now calculate pH:
Why the corrected pH is less than 7 but still close to neutral
This result makes chemical sense. The solution does contain a strong acid, so the pH should be below 7. But the acid is extremely dilute, so it only nudges the hydrogen ion concentration above the pure-water value. That is why the pH is only slightly acidic. The corrected hydrogen ion concentration, about 1.161×10^-7 M, is only modestly larger than 1.0×10^-7 M.
This is a classic example of how equilibrium chemistry protects you from impossible answers. The naive method gave 7.52, suggesting a basic solution even though you added acid. Once water autoionization is included, the result shifts to a physically meaningful value.
Common mistakes students make
- Using pH = -log C without thinking: This is the most frequent error in dilute strong-acid problems.
- Forgetting water contributes H+ and OH-: At concentrations near 10^-7 M, this effect is no longer negligible.
- Choosing the wrong quadratic root: Only the positive concentration is physically meaningful.
- Confusing formal concentration with equilibrium [H+]: In dilute cases, they are not identical.
- Rounding too early: Keep extra digits until the final pH value.
Quick comparison: naive vs corrected method
The table below shows why the corrected method matters so much at very low acid concentrations. The corrected values are based on the exact quadratic expression using Kw = 1.0×10^-14 at 25 C.
| HBr concentration (M) | Naive pH = -log C | Corrected [H+] (M) | Corrected pH | Difference in pH units |
|---|---|---|---|---|
| 1.0×10^-3 | 3.000 | 1.00000001×10^-3 | 3.000 | Approximately 0.000 |
| 1.0×10^-6 | 6.000 | 1.0099×10^-6 | 5.996 | 0.004 |
| 1.0×10^-7 | 7.000 | 1.618×10^-7 | 6.791 | 0.209 |
| 3.0×10^-8 | 7.523 | 1.161×10^-7 | 6.935 | 0.588 |
| 1.0×10^-8 | 8.000 | 1.051×10^-7 | 6.978 | 1.022 |
Interpretation of the data
The statistics in the table reveal an important trend. At 10^-3 M, the acid is so much stronger in concentration than water’s own hydrogen ion contribution that the corrected and naive values are effectively identical. But as you approach 10^-7 M and below, the discrepancy grows rapidly. At 3.0×10^-8 M, the error exceeds half a pH unit, which is very large in acid-base chemistry.
This pattern is not unique to HBr. The same logic applies to other strong acids such as HCl, HNO3, and HI when they are present at very low concentrations. The exact pH depends on temperature because Kw changes with temperature, but the reasoning remains the same.
How to know when the shortcut is safe
- If the strong acid concentration is much larger than 1.0×10^-7 M at 25 C, the shortcut usually works.
- If the concentration is in the neighborhood of 10^-7 M or lower, check whether water autoionization matters.
- If the naive pH comes out near 7 or above 7 for an acid solution, stop and reassess immediately.
- For high-precision work, solve the full equation rather than relying on approximations.
Reference values that help build intuition
Students often remember the method more easily if they compare it with familiar pH benchmarks. The following table places the corrected answer in context.
| System or concentration | Approximate pH at 25 C | Meaning |
|---|---|---|
| Pure water | 7.00 | Neutral benchmark with [H+] = [OH-] = 1.0×10^-7 M |
| 3.0×10^-8 M HBr, corrected | 6.94 | Slightly acidic because acid raises total [H+] above water’s baseline |
| 1.0×10^-7 M HBr, corrected | 6.79 | Acid and water contributions are strongly intertwined |
| 1.0×10^-6 M HBr, corrected | 6.00 | Water contribution is small but still present |
| 1.0×10^-3 M HBr | 3.00 | Typical strong-acid behavior where the shortcut is reliable |
Why this matters in real chemistry
Very dilute acid solutions appear in environmental chemistry, analytical chemistry, instrument calibration, and introductory lab discussions of pH measurement limits. In practice, real measured pH values can also be influenced by ionic strength, dissolved carbon dioxide, activity effects, and electrode behavior. Still, for a standard general chemistry calculation at 25 C, the corrected quadratic method is the accepted solution.
If you want to review reliable background information on pH and aqueous chemistry, useful authoritative resources include the U.S. Environmental Protection Agency explanation of pH measurement, the NIST Chemistry WebBook, and educational acid-base materials from universities such as LibreTexts chemistry resources used by many colleges. These references help place the calculation in a broader scientific context.
Short exam-ready solution
If you need a concise answer for homework or a test, you can write it like this:
Final takeaway
To calculate the pH of a 3.0×10^-8 M solution of HBr correctly, do not use the simplistic pH = -log C formula by itself. Because the acid concentration is extremely low, water autoionization contributes significantly to the total hydrogen ion concentration. The exact calculation gives a hydrogen ion concentration of about 1.161×10^-7 M and a pH of about 6.94. That answer is chemically consistent, mathematically correct, and far more accurate than the naive result.