Calculate the pH of 9.09 × 10-2 M HBr
Use this premium chemistry calculator to find the pH of hydrobromic acid from scientific notation concentration values. HBr is a strong acid, so for typical general chemistry problems its hydrogen ion concentration is taken as equal to the acid molarity. Enter the coefficient and exponent to calculate pH instantly and visualize the result on a chart.
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Default example loaded: calculate the pH of 9.09 × 10^-2 M HBr.
Expert guide: how to calculate the pH of 9.09 × 10-2 M HBr
When a chemistry problem asks you to calculate the pH of 9.09 × 10-2 M HBr, the key idea is recognizing that hydrobromic acid is classified as a strong acid in aqueous solution. In an introductory or general chemistry setting, strong acids are treated as completely dissociated. That means each mole of HBr produces one mole of H+ ions and one mole of Br– ions. Because HBr is monoprotic, the hydrogen ion concentration is numerically equal to the original acid concentration.
So if the concentration of HBr is 9.09 × 10-2 M, then the hydrogen ion concentration is also 9.09 × 10-2 M. Once that step is clear, the pH calculation becomes straightforward. The pH formula is:
Substitute the concentration into the equation:
Evaluating this gives a pH of about 1.04. This is a strongly acidic solution, which makes sense because the hydrogen ion concentration is much larger than 1.0 × 10-7 M, the reference concentration associated with neutral water at 25°C.
Step by step solution
- Identify the acid: HBr, or hydrobromic acid.
- Recall that HBr is a strong acid, so it dissociates essentially completely in water.
- Set hydrogen ion concentration equal to acid concentration: [H+] = 9.09 × 10-2 M.
- Use the pH formula: pH = -log10[H+].
- Calculate: pH = -log10(0.0909) ≈ 1.041.
- Report the answer with appropriate significant figures: pH ≈ 1.04.
This is the full reasoning behind the answer. Students often try to overcomplicate strong acid problems, but for HBr at this concentration, the simple complete dissociation model is exactly what most coursework expects.
Why HBr is treated as a strong acid
Hydrobromic acid belongs to the common set of strong acids taught in first year chemistry. Other examples include HCl, HI, HNO3, HClO4, and the first dissociation of H2SO4. In water, these acids donate protons so extensively that equilibrium lies very far toward products. For practical pH calculations at ordinary concentrations, we approximate the dissociation as complete.
That assumption gives a reliable result here because 9.09 × 10-2 M is not a dilute trace level where autoionization of water becomes important, and it is not in an advanced nonideal regime where activity corrections dominate a basic homework problem. In other words, the standard classroom method is fully appropriate.
Converting scientific notation into decimal form
Some learners get stuck not on the chemistry, but on the scientific notation. The expression 9.09 × 10-2 means move the decimal two places to the left:
- 9.09 × 10-1 = 0.909
- 9.09 × 10-2 = 0.0909
- 9.09 × 10-3 = 0.00909
So 9.09 × 10-2 M is exactly 0.0909 M. Then the pH is simply the negative base 10 logarithm of 0.0909. If you enter that on a calculator, you should get about 1.0414, which rounds to 1.04.
Significant figures and pH reporting
pH values follow a common reporting convention tied to the number of significant figures in the concentration. The value 9.09 has three significant figures. Therefore, the pH should usually be reported with three digits after the decimal if your instructor is enforcing strict logarithm rules, giving 1.041. In many classroom and online examples, it is also acceptable to round to 1.04. If precision matters, check your course expectations.
| Input concentration | Decimal molarity | [H+] for strong monoprotic acid | Calculated pH |
|---|---|---|---|
| 9.09 × 10-1 M | 0.909 M | 0.909 M | 0.041 |
| 9.09 × 10-2 M | 0.0909 M | 0.0909 M | 1.041 |
| 9.09 × 10-3 M | 0.00909 M | 0.00909 M | 2.041 |
| 9.09 × 10-4 M | 0.000909 M | 0.000909 M | 3.041 |
This table shows a useful pattern: every tenfold decrease in hydrogen ion concentration increases the pH by 1 unit. That is the hallmark of the logarithmic pH scale.
What the answer means chemically
A pH of about 1.04 indicates a highly acidic solution. The pH scale is logarithmic, not linear, so a solution at pH 1 is much more acidic than a solution at pH 2. In fact, the pH 1 solution has roughly 10 times greater hydrogen ion concentration than a pH 2 solution. This is why the pH number changes slowly while the chemistry changes dramatically.
For 9.09 × 10-2 M HBr, the bromide ion concentration would also be 9.09 × 10-2 M because each HBr molecule splits into one H+ and one Br– ion. That means the major dissolved species after dissociation are water, H+ represented more accurately as hydronium in water, and bromide ions.
Common mistakes students make
- Forgetting that HBr is strong. Some students try to build an ICE table and solve an equilibrium expression. For this level, that is unnecessary.
- Using pOH instead of pH. Since the problem gives an acid, start with pH = -log[H+].
- Mishandling the negative exponent. 10-2 means divide by 100, not multiply by 100.
- Dropping the negative sign in the logarithm formula. The pH formula always includes the leading minus sign.
- Reporting too many digits. Round sensibly based on the concentration given.
Comparison of strong acid concentrations and pH
The pH scale is often easier to understand when viewed across several concentrations. Below is a comparison table showing how concentration and pH move together for a strong monoprotic acid like HBr or HCl under the same introductory assumptions.
| Strong acid molarity | Hydrogen ion concentration | pH | Acidity relative to 9.09 × 10-2 M HBr |
|---|---|---|---|
| 1.00 × 10-1 M | 0.100 M | 1.000 | About 1.10 times more concentrated in H+ |
| 9.09 × 10-2 M | 0.0909 M | 1.041 | Reference case |
| 1.00 × 10-2 M | 0.0100 M | 2.000 | About 9.09 times less concentrated in H+ |
| 1.00 × 10-3 M | 0.00100 M | 3.000 | About 90.9 times less concentrated in H+ |
How this problem appears in homework and exams
In many chemistry classes, instructors phrase this exact type of question in a compact form: “Calculate the pH of 9.09 × 10-2 M HBr.” The point is usually to test three skills at once: recognizing a strong acid, handling scientific notation, and applying the logarithm definition of pH. If you can complete those three steps reliably, you will solve a large portion of early acid-base problems correctly.
A fast exam approach looks like this:
- HBr is strong, so [H+] = 9.09 × 10-2.
- pH = -log(9.09 × 10-2).
- Answer ≈ 1.04.
Real reference points for pH interpretation
While textbook HBr solutions are laboratory chemicals and not everyday household substances, the pH scale itself is widely used in environmental science, water quality, biology, and industrial chemistry. Pure water at 25°C is near pH 7. Many natural waters are considered acceptable in a moderate range around neutral, while much lower pH values indicate strongly acidic conditions. A pH around 1 is far outside normal environmental water conditions and signals a corrosive acidic solution.
For perspective, water quality references from public agencies often discuss acceptable pH ranges for drinking water or environmental systems. Those values are nowhere near pH 1 because such an acidic solution would be hazardous. That comparison reinforces why 9.09 × 10-2 M HBr should be treated with appropriate laboratory caution.
Authoritative chemistry and water quality sources
If you want to verify core concepts, review acid-base fundamentals, or compare pH with real water quality standards, these authoritative resources are useful:
- U.S. Environmental Protection Agency: pH overview
- U.S. Geological Survey: pH and water
- LibreTexts Chemistry educational resource
Final answer
To calculate the pH of 9.09 × 10-2 M HBr, assume complete dissociation because HBr is a strong monoprotic acid. Therefore:
- [H+] = 9.09 × 10-2 M
- pH = -log10(9.09 × 10-2)
- pH ≈ 1.04
If you use the calculator above, you can also test nearby concentrations, compare the pH visually, and better understand how scientific notation affects acidity on the logarithmic pH scale.