Calculate the pH for H3O+ = 7.5 × 10-10 M
Use this interactive calculator to compute pH, pOH, and classify the solution from a hydronium ion concentration written in scientific notation.
pH Calculator
Formula used: pH = -log10[H3O+]. At 25 C, pOH = 14.00 – pH.
How to calculate the pH for H3O+ = 7.5 × 10-10 M
If your chemistry assignment asks you to calculate the pH for a hydronium ion concentration of 7.5 × 10-10 M, the core skill you need is converting scientific notation into a logarithmic pH value. The good news is that the process is short, reliable, and based on one of the most important equations in acid-base chemistry. Hydronium concentration directly measures how acidic a solution is, and pH is simply a compact way of expressing that concentration on a logarithmic scale.
For this problem, the given concentration is very small, which means the solution is not strongly acidic. In fact, because 7.5 × 10-10 M is less than 1.0 × 10-7 M at 25 C, the calculated pH will be greater than 7. That indicates a slightly basic solution. Many students assume anything involving H3O+ must be acidic, but the relative concentration matters more than the mere presence of hydronium. Water always contains some hydronium and hydroxide due to autoionization.
The formula you need
The standard equation for pH is:
pH = -log10([H3O+])Here, [H3O+] means the hydronium ion concentration in moles per liter, also written as mol/L or M. In this problem:
- [H3O+] = 7.5 × 10-10 M
- pH = -log10(7.5 × 10-10)
Step by step solution
- Write down the formula: pH = -log10([H3O+]).
- Substitute the value: pH = -log10(7.5 × 10-10).
- Break the logarithm apart using log(ab) = log(a) + log(b).
- So, log10(7.5 × 10-10) = log10(7.5) + log10(10-10).
- Since log10(7.5) ≈ 0.8751 and log10(10-10) = -10, the total is 0.8751 – 10 = -9.1249.
- Apply the negative sign outside the logarithm: pH = -(-9.1249) = 9.1249.
- Round appropriately: pH ≈ 9.12 or 9.125 depending on required precision.
This is the exact reasoning your teacher expects to see. If you are using a calculator, you can enter the concentration directly in scientific notation and then apply the negative logarithm. On many scientific calculators, that means pressing the log key and then changing the sign at the end, or using a dedicated negative sign before the logarithm result.
Why the pH is above 7
At 25 C, neutral water has a hydronium concentration of 1.0 × 10-7 M and a pH of 7.00. If a solution has a hydronium concentration lower than 1.0 × 10-7 M, then it must have a pH greater than 7, which means it is basic. Since 7.5 × 10-10 M is much smaller than 1.0 × 10-7 M, the resulting pH is significantly above neutral.
This can feel counterintuitive at first because students often think of H3O+ as automatically producing an acidic answer. In reality, acidity and basicity are always relative. A basic solution still contains hydronium ions, just at a lower concentration than neutral water does. At the same time, it contains a higher hydroxide concentration.
Finding pOH too
Once the pH is known, you can usually find pOH from the relationship:
pH + pOH = 14.00 at 25 CUsing pH = 9.1249:
- pOH = 14.00 – 9.1249
- pOH = 4.8751
That tells you the hydroxide concentration is relatively high compared with hydronium, which confirms the solution is basic. If needed, you can also calculate [OH-] using:
[OH-] = 10-pOHSubstituting pOH = 4.8751 gives [OH-] ≈ 1.33 × 10-5 M. This is much greater than 1.0 × 10-7 M, which is another sign of a basic solution.
Common mistakes when solving this pH problem
Even though the calculation is straightforward, students make several recurring errors. Avoiding these mistakes can improve both speed and accuracy.
- Forgetting the negative sign: pH is the negative logarithm of hydronium concentration. Missing the negative sign gives the wrong sign and an impossible pH.
- Misreading scientific notation: 7.5 × 10-10 is not the same as 7.5 × 1010. The negative exponent means a very small number.
- Calling the solution acidic: Because the hydronium concentration is below 1.0 × 10-7 M, the solution is basic, not acidic.
- Rounding too early: Keep enough digits during intermediate steps, then round the final pH to the requested precision.
- Using pH = log[H3O+]: The correct equation includes a negative sign.
Comparison table: pH values from different hydronium concentrations
The table below helps place 7.5 × 10-10 M in context. These values are computed from pH = -log10[H3O+], assuming 25 C.
| Hydronium concentration [H3O+] | Calculated pH | Classification | Interpretation |
|---|---|---|---|
| 1.0 × 10-1 M | 1.00 | Strongly acidic | High hydronium concentration, common in strong acid solutions. |
| 1.0 × 10-3 M | 3.00 | Acidic | Acidic but much weaker than pH 1 solutions. |
| 1.0 × 10-7 M | 7.00 | Neutral | Ideal neutral point for pure water at 25 C. |
| 7.5 × 10-10 M | 9.125 | Slightly basic | Less hydronium than neutral water, so pH is above 7. |
| 1.0 × 10-12 M | 12.00 | Basic | Very low hydronium and high hydroxide concentration. |
Real reference data about water chemistry and pH
When learning pH, it helps to compare textbook values to observed environmental and chemical data. The figures below are widely cited in chemistry and water quality education. They show why a pH around 9.1 is considered basic but not extraordinarily extreme.
| Reference statistic | Typical value | Why it matters |
|---|---|---|
| Neutral water at 25 C | pH 7.00, [H3O+] = 1.0 × 10-7 M | This is the benchmark used in most general chemistry problems. |
| Natural water commonly observed by USGS | About pH 6.5 to 8.5 | Shows that most environmental waters cluster near neutral, not at extreme pH values. |
| EPA secondary drinking water guidance range | pH 6.5 to 8.5 | Helps students see that pH near 9.1 is somewhat above the common aesthetic drinking-water range. |
| Ion product of water at 25 C | Kw = 1.0 × 10-14 | Supports the relation pH + pOH = 14.00 at 25 C. |
How scientific notation affects the pH answer
Scientific notation makes pH calculations easier once you understand logarithms. The exponent mostly controls the size of the pH, while the coefficient fine-tunes it. In the concentration 7.5 × 10-10, the exponent of -10 suggests the pH will be near 10, and the coefficient 7.5 slightly lowers it from 10 to about 9.125. This is because log10(7.5) is positive, and the negative sign in the pH formula subtracts that portion from the final number.
A useful shortcut is this:
- If [H3O+] = a × 10-b, then pH = b – log10(a).
- For this problem, a = 7.5 and b = 10.
- So pH = 10 – log10(7.5) = 10 – 0.8751 = 9.1249.
This shortcut is mathematically equivalent to the longer logarithm breakdown and often makes hand calculations faster on exams.
What this result means in practical chemistry
A pH of about 9.125 represents a mildly basic solution. It is not as basic as concentrated sodium hydroxide, but it is clearly above neutral. In classroom chemistry, this kind of pH might appear in a dilute base problem, a hydrolysis problem involving a weak base salt, or a conceptual question about comparing ion concentrations.
It also shows the power of the pH scale. A shift of just a few pH units corresponds to enormous changes in hydronium concentration. Because the scale is logarithmic, each whole pH unit reflects a tenfold change in [H3O+]. So a solution at pH 9 has one hundred times less hydronium than a solution at pH 7.
Key takeaways
- The formula is pH = -log10([H3O+]).
- For [H3O+] = 7.5 × 10-10 M, the pH is about 9.125.
- Because pH is greater than 7, the solution is basic.
- At 25 C, pOH is about 4.875.
- The coefficient affects the decimal portion of pH, while the exponent determines the general size of the answer.
Authoritative resources for deeper study
USGS: pH and Water
U.S. EPA: pH Overview
Florida State University: pH and pH Paper Basics
Final answer
To calculate the pH for H3O+ = 7.5 × 10-10 M, apply the formula pH = -log10([H3O+]). The result is:
pH = 9.125That means the solution is slightly basic at 25 C.