Calculate the pH of 9.02 × 10^-5 M Ba(OH)2
Enter the concentration in scientific notation, confirm the hydroxide ions released per formula unit, and instantly compute hydroxide concentration, pOH, and pH.
How to calculate the pH of 9.02 × 10^-5 M Ba(OH)2
To calculate the pH of 9.02 × 10^-5 M Ba(OH)2, you begin by recognizing that barium hydroxide is a strong base. In introductory and most general chemistry settings, strong bases are treated as completely dissociated in water. That means each formula unit of Ba(OH)2 contributes one barium ion, Ba2+, and two hydroxide ions, OH-. Since pH is linked to hydrogen ion concentration and pOH is linked to hydroxide ion concentration, the problem is really about converting the given molarity of Ba(OH)2 into the hydroxide ion concentration and then using logarithms.
The concentration written as 9.02 × 10^-5 M means the solution contains 0.0000902 moles of Ba(OH)2 per liter. Because each mole of Ba(OH)2 gives 2 moles of OH-, the hydroxide concentration is:
[OH-] = 2 × 9.02 × 10^-5 = 1.804 × 10^-4 MOnce you know [OH-], find the pOH:
pOH = -log10(1.804 × 10^-4) ≈ 3.744At 25 degrees C, pH and pOH are related by a simple identity:
pH = 14.000 – 3.744 = 10.256So the pH of 9.02 × 10^-5 M Ba(OH)2 is approximately 10.26. That is the final answer to two decimal places. This value confirms the solution is basic, as expected, because its pH is greater than 7.00.
Fast answer
- Given concentration of Ba(OH)2 = 9.02 × 10^-5 M
- Hydroxide ions per mole of Ba(OH)2 = 2
- [OH-] = 1.804 × 10^-4 M
- pOH ≈ 3.744
- pH ≈ 10.256
- Rounded pH = 10.26
Why the factor of 2 matters
Students often make a very common mistake with metal hydroxides such as Ba(OH)2, Ca(OH)2, and Sr(OH)2. They use the molarity of the compound directly as the hydroxide concentration. That approach is incorrect for bases that release more than one hydroxide ion per formula unit. Since Ba(OH)2 has two hydroxides in its chemical formula, every mole of dissolved base contributes twice as many moles of hydroxide ions.
If you ignored that factor and used 9.02 × 10^-5 M directly as [OH-], you would get a pOH that is too high and a pH that is too low. The correct stoichiometric conversion is what gives the accurate answer.
Step by step chemistry method
1. Write the dissociation equation
For a strong base such as barium hydroxide, the dissociation can be written as:
Ba(OH)2(aq) → Ba2+(aq) + 2OH-(aq)This equation tells you the mole ratio between Ba(OH)2 and OH- is 1:2.
2. Convert compound concentration to hydroxide concentration
Multiply the molarity of Ba(OH)2 by 2:
[OH-] = 2(9.02 × 10^-5) = 1.804 × 10^-4 M3. Calculate pOH
Use the definition of pOH:
pOH = -log10[OH-]Substituting the hydroxide concentration:
pOH = -log10(1.804 × 10^-4) ≈ 3.7444. Convert pOH to pH
At 25 degrees C, use:
pH + pOH = 14.00So:
pH = 14.00 – 3.744 = 10.2565. Apply correct rounding
Because the given concentration has three significant figures, reporting the pH as 10.26 is usually appropriate in general chemistry coursework.
Summary checklist
- Identify whether the solute is a strong acid or strong base.
- Use the dissociation stoichiometry from the chemical formula.
- Compute [OH-] or [H3O+].
- Take the negative base-10 logarithm.
- Convert between pOH and pH if needed.
- Round to a sensible number of decimal places.
Important concepts behind this pH calculation
Strong base behavior
Barium hydroxide is categorized as a strong base in many chemistry courses, which means it is considered to dissociate essentially completely in water under ordinary conditions. That simplifies the problem because the equilibrium calculation usually required for weak bases is not necessary here. Instead of using a base dissociation constant, Kb, you directly determine the hydroxide concentration from stoichiometry.
Scientific notation in chemistry
The notation 9.02 × 10^-5 is standard for concentrations that are much smaller than 1. In decimal form, it is 0.0000902. Converting between scientific notation and decimal notation correctly is an essential skill because pH calculations frequently involve values like 10^-3, 10^-5, or 10^-8. In this case, after accounting for the two hydroxide ions, the hydroxide concentration becomes 1.804 × 10^-4 M, which is 0.0001804 M.
Why pH is above 10
Even though 9.02 × 10^-5 M may look like a small concentration, hydroxide concentrations around 10^-4 M still produce noticeably basic solutions. Neutral water at 25 degrees C has [H3O+] = 1.0 × 10^-7 M and [OH-] = 1.0 × 10^-7 M. Here, the hydroxide concentration is around 1.804 × 10^-4 M, which is roughly 1,804 times larger than the hydroxide concentration in neutral water. That is why the pH is pushed well above 7.00 and lands around 10.26.
When water autoionization matters
At very low acid or base concentrations, the autoionization of water can become significant. Water naturally contributes about 1.0 × 10^-7 M of both H3O+ and OH- at 25 degrees C. For a strong base concentration that is much larger than 10^-7 M, the contribution from water is usually negligible. Since the hydroxide concentration here is 1.804 × 10^-4 M, it is far greater than 10^-7 M, so ignoring water autoionization is justified in a standard chemistry calculation.
Comparison tables and reference data
Table 1: Strong base concentration compared with resulting pOH and pH
| Base and concentration | OH- per formula unit | Calculated [OH-] (M) | pOH | pH at 25 degrees C |
|---|---|---|---|---|
| NaOH, 1.00 × 10^-5 M | 1 | 1.00 × 10^-5 | 5.000 | 9.000 |
| Ba(OH)2, 9.02 × 10^-5 M | 2 | 1.804 × 10^-4 | 3.744 | 10.256 |
| Ca(OH)2, 1.00 × 10^-4 M | 2 | 2.00 × 10^-4 | 3.699 | 10.301 |
| KOH, 1.00 × 10^-3 M | 1 | 1.00 × 10^-3 | 3.000 | 11.000 |
This table shows how stoichiometry changes the final pH. Notice that Ba(OH)2 at 9.02 × 10^-5 M gives a pH above 10 because the hydroxide concentration doubles relative to the formula concentration.
Table 2: Typical pH ranges of familiar substances
| Substance or water type | Typical pH range | Interpretation |
|---|---|---|
| Battery acid | 0 to 1 | Extremely acidic |
| Black coffee | 4.8 to 5.2 | Mildly acidic |
| Pure water at 25 degrees C | 7.0 | Neutral |
| Seawater | 7.5 to 8.4 | Slightly basic |
| Household ammonia | 11 to 12 | Basic |
| Calculated 9.02 × 10^-5 M Ba(OH)2 solution | 10.26 | Moderately basic |
The calculated pH of 10.26 places this solution comfortably in the basic range, though it is still less basic than many concentrated cleaning solutions.
Common mistakes students make
Using the wrong ion concentration
The most frequent error is treating 9.02 × 10^-5 M as [OH-] instead of as the concentration of Ba(OH)2. Because each unit releases two hydroxide ions, [OH-] must be doubled.
Confusing pH with pOH
Another common error is to stop after taking the logarithm and report pOH as if it were the pH. For this problem, 3.744 is pOH, not pH. Since the solution is basic, the pH must be greater than 7. The final pH is 10.256.
Dropping the negative sign in the logarithm
By definition, pOH = -log10[OH-]. Because the logarithm of a number less than 1 is negative, the leading negative sign is necessary to make pOH positive.
Ignoring temperature assumptions
The relation pH + pOH = 14.00 is exact only at 25 degrees C in most textbook contexts. If temperature changes significantly, the ionic product of water changes as well. For standard homework and exam problems, however, 25 degrees C is usually assumed unless another temperature is specified.
Rounding too early
If you round 1.804 × 10^-4 to 1.8 × 10^-4 too early, the final pH shifts slightly. It is best practice to carry extra digits through the calculation and round only at the end.
Practical interpretation of the result
A pH of 10.26 means the solution is definitely basic and would turn many acid-base indicators toward their basic color range. It is not as aggressively basic as concentrated sodium hydroxide or drain cleaner, but it is still alkaline enough to require proper laboratory handling. Barium compounds also carry toxicological concerns, so real laboratory work involving Ba(OH)2 should follow institutional safety procedures and material safety guidelines.
From an educational perspective, this example is especially useful because it combines three foundational chemistry skills in one compact problem: reading scientific notation, applying stoichiometric dissociation, and using logarithmic definitions. If a student can solve this correctly, they are demonstrating solid understanding of both acid-base chemistry and quantitative problem solving.
What this value means numerically
- The hydroxide concentration is 1.804 × 10^-4 M.
- The solution is far more basic than neutral water.
- The pH is 3.26 units above neutral, which corresponds to a large logarithmic difference.
- Compared with a pH 9 solution, a pH 10.26 solution is over 18 times lower in hydronium concentration because each pH unit is a factor of 10.
Authoritative references and further reading
For readers who want to cross-check acid-base concepts, logarithms, and pH fundamentals using highly credible sources, these references are excellent places to start:
- U.S. Environmental Protection Agency: pH basics and water quality context
- Chemistry LibreTexts: acid-base calculations and pH relationships
- NIST Chemistry WebBook: authoritative chemistry data resources
While the EPA source gives a practical pH context for environmental science, LibreTexts and NIST are useful for reinforcing the definitions and chemical conventions used in classroom calculations.
Final conclusion
If you are asked to calculate the pH of 9.02 × 10^-5 M Ba(OH)2, the correct textbook method is straightforward. First, double the given molarity because barium hydroxide releases two hydroxide ions. That gives [OH-] = 1.804 × 10^-4 M. Next, calculate pOH as 3.744. Finally, subtract from 14.00 at 25 degrees C to obtain pH = 10.256, or about 10.26. Any answer near 10.26 is consistent with correct chemistry and proper logarithmic handling.