Calculate the pH of 9.09 × 10-2 M HBr
Use this interactive calculator to solve the pH of hydrobromic acid solutions instantly. For the target problem, 9.09 × 10-2 M HBr is a strong acid solution, so it dissociates essentially completely and gives a pH of about 1.04.
Strong Acid pH Calculator
Enter the concentration in scientific notation and select the acid type. The default values are set to the problem: 9.09 × 10-2 M HBr.
Interpretation of the problem statement: “9.09 10 2m hbr” is typically read as 9.09 × 10-2 M HBr.
Results
Click Calculate pH to see the full solution.
How this calculator solves the problem
- Converts the scientific notation input into molarity.
- Uses complete dissociation for strong acids like HBr.
- Sets [H+] = acid concentration for HBr.
- Applies the pH equation: pH = -log10[H+].
[H+] = 9.09 × 10^-2 = 0.0909 MpH = -log10(0.0909) ≈ 1.0414
Expert Guide: How to Calculate the pH of 9.09 × 10-2 M HBr
If you need to calculate the pH of 9.09 × 10-2 M HBr, the chemistry is straightforward once you recognize that hydrobromic acid is a strong acid. In water, HBr dissociates essentially completely into hydrogen ions and bromide ions. That means the hydrogen ion concentration is taken to be the same as the acid concentration for a standard general chemistry calculation. Because pH depends on hydrogen ion concentration, this type of problem is one of the most direct acid-base calculations you will encounter.
The notation in the prompt is often typed informally as “9.09 10 2m hbr,” but in scientific form it is usually written as 9.09 × 10-2 M HBr. The negative exponent matters. It tells you that the concentration is less than 1 molar, specifically 0.0909 M. Once that number is clear, the rest of the work follows from the pH equation.
Step 1: Identify whether HBr is strong or weak
Hydrobromic acid is classified as a strong acid in aqueous solution. Strong acids dissociate almost completely. In practical introductory chemistry, that means you can write:
HBr → H+ + Br–
Since one mole of HBr produces one mole of H+, HBr is also monoprotic. Therefore:
[H+] = [HBr]
This is the key shortcut. You do not need an equilibrium table for this problem, and you do not need to solve for partial dissociation. That is what makes strong-acid pH problems faster than weak-acid problems.
Step 2: Convert the scientific notation to decimal form
The concentration is:
9.09 × 10-2 M
A power of 10 with exponent -2 moves the decimal point two places to the left:
9.09 × 10-2 = 0.0909
So the molarity of the acid is 0.0909 M. Since HBr fully dissociates:
[H+] = 0.0909 M
Step 3: Apply the pH formula
The definition of pH is:
pH = -log10[H+]
Substitute the hydrogen ion concentration:
pH = -log10(0.0909)
Evaluating the logarithm gives:
pH ≈ 1.0414
Rounded appropriately:
- pH = 1.04 to two decimal places
- pH = 1.041 to three decimal places
Why the answer is not 2
A common mistake is to look at the exponent -2 and assume the pH should simply be 2. That shortcut only works when the concentration is exactly a clean power of ten, such as 1.0 × 10-2 M, because:
-log(1.0 × 10-2) = 2.00
But here the coefficient is 9.09, not 1.00. Since 9.09 × 10-2 is much larger than 1.0 × 10-2, the solution is more acidic, and its pH must be lower than 2. That is why the correct answer is about 1.04.
Full worked solution in compact form
- Given concentration: 9.09 × 10-2 M HBr
- HBr is a strong monoprotic acid, so [H+] = 9.09 × 10-2 M
- Convert to decimal: [H+] = 0.0909 M
- Use pH formula: pH = -log(0.0909)
- Result: pH ≈ 1.04
Comparison table: pH values for nearby strong acid concentrations
The table below helps you compare the target concentration with nearby values. This is useful for checking whether your answer is reasonable.
| Strong acid concentration, [H+] (M) | Scientific notation | Calculated pH | Interpretation |
|---|---|---|---|
| 1.0 | 1.0 × 100 | 0.00 | Extremely acidic benchmark solution |
| 0.100 | 1.0 × 10-1 | 1.00 | Classic textbook strong acid example |
| 0.0909 | 9.09 × 10-2 | 1.041 | Your HBr problem value |
| 0.0100 | 1.0 × 10-2 | 2.00 | Ten times less acidic than 0.100 M |
| 0.00100 | 1.0 × 10-3 | 3.00 | Still acidic, but substantially diluted |
What happens chemically in solution?
When HBr dissolves in water, it transfers its proton to water molecules, producing hydronium ions. In simplified notation, many classes write H+, but the more realistic aqueous species is H3O+. The practical outcome for pH is the same: the concentration of acidic species is set by how much HBr was dissolved.
This also means the bromide ion, Br–, acts mostly as a spectator ion in the pH calculation. It balances charge but does not significantly affect the acidity in the same direct way. So if your only goal is pH, you focus on the hydronium concentration generated by HBr.
Significant figures and reporting the answer correctly
Because the concentration 9.09 × 10-2 has three significant figures, a careful lab-style report often keeps the pH to three digits after the decimal when carrying full precision, then rounds according to your instructor’s rules. In many homework settings, 1.04 is the expected answer. In more exact reporting, 1.041 may be acceptable.
A useful pH reporting rule is that the number of decimal places in the pH often corresponds to the number of significant figures in the concentration. That is why 0.0909 M, which has three significant figures, can justify a pH written to three decimal places.
Second data table: pH scale context for interpreting 1.04
A pH of 1.04 is very acidic. The comparison table below places the result in familiar context.
| Substance or reference range | Typical pH | How it compares with 9.09 × 10-2 M HBr |
|---|---|---|
| Battery acid reference region | About 0 to 1 | Very similar acidity range |
| 1.0 × 10-1 M strong acid | 1.00 | Nearly identical to this problem |
| Your HBr solution | 1.04 | Strongly acidic |
| Lemon juice | About 2 to 3 | Your HBr solution is substantially more acidic |
| Pure water at 25°C | 7.00 | Neutral reference point, far less acidic |
Common student errors when solving this problem
- Ignoring the coefficient 9.09 and using only the exponent. This gives the wrong pH.
- Treating HBr as a weak acid. In standard general chemistry, HBr is strong.
- Forgetting the negative sign in the pH formula. Since logs of numbers less than 1 are negative, the extra negative sign is essential.
- Misreading the notation. 9.09 × 10-2 M is 0.0909 M, not 9.09 M and not 0.00909 M.
- Using natural log instead of log base 10. pH uses log10.
Quick mental check
You can estimate the result before calculating. Since 0.0909 M is just a little less than 0.100 M, and 0.100 M strong acid has pH 1.00, your answer should be just a little above 1.00. That makes 1.04 very plausible. This kind of estimation is valuable on exams because it helps you catch keystroke errors.
Formula summary for strong acid pH problems
- For a strong monoprotic acid like HBr: [H+] = C
- Then calculate: pH = -log10(C)
- For the given problem: pH = -log10(9.09 × 10-2) = 1.04
Authoritative chemistry and pH references
If you want to verify pH concepts and acid-base fundamentals using authoritative educational and government sources, these references are excellent starting points:
- U.S. Environmental Protection Agency: pH and Water
- Chemistry educational resource hub for acid-base topics
- NIST Chemistry WebBook
Note: The pH comparison ranges above are educational reference values commonly used in chemistry instruction and may vary slightly with temperature, activity effects, and source conventions. Introductory calculations typically assume ideal dilute behavior and complete dissociation for HBr.
Bottom line
To calculate the pH of 9.09 × 10-2 M HBr, convert the concentration to 0.0909 M, recognize that HBr is a strong monoprotic acid, set the hydrogen ion concentration equal to 0.0909 M, and compute pH = -log(0.0909). The result is 1.04. If you remember that 0.100 M strong acid has pH 1.00, this answer is also easy to confirm by estimation.