Calculate the pH of 0.0046 M Ba(OH)2
Use this premium calculator to find hydroxide concentration, pOH, and pH for barium hydroxide solutions. The default example is 0.0046 M Ba(OH)2, a classic strong-base stoichiometry problem.
Ba(OH)2 pH Calculator
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Enter or keep the default value of 0.0046 M for Ba(OH)2, then click Calculate pH.
Visual Breakdown
This chart compares the base molarity, hydroxide ion concentration, pOH, and pH generated from your input.
How to calculate the pH of 0.0046 M Ba(OH)2
To calculate the pH of 0.0046 M barium hydroxide, you use the fact that Ba(OH)2 is treated as a strong base in introductory chemistry. That means it dissociates essentially completely in water into one barium ion and two hydroxide ions:
Ba(OH)2 → Ba2+ + 2OH–
The concentration of hydroxide ions is therefore twice the concentration of the dissolved Ba(OH)2. Starting from 0.0046 M barium hydroxide:
[OH–] = 2 × 0.0046 = 0.0092 M
Next, compute pOH using the base-10 logarithm:
pOH = -log(0.0092) ≈ 2.036
At 25 C, pH and pOH add up to 14.00, so:
pH = 14.00 – 2.036 = 11.964
So the pH of a 0.0046 M Ba(OH)2 solution is approximately 11.96.
Step-by-step method
- Write the dissociation equation: Ba(OH)2 → Ba2+ + 2OH–.
- Identify the base concentration: 0.0046 M.
- Multiply by 2 because each unit gives two hydroxide ions.
- Find [OH–] = 0.0092 M.
- Calculate pOH = -log[OH–] = -log(0.0092).
- Compute pH = 14 – pOH.
- Report the answer with suitable rounding: pH ≈ 11.96.
Why Ba(OH)2 changes the calculation
Students often learn pH calculations first with monoprotic strong bases such as NaOH and KOH. For those compounds, one mole of base gives one mole of hydroxide ions, so the hydroxide concentration equals the listed molarity. Barium hydroxide is different because every formula unit contains two hydroxide groups. That structural detail is the entire key to this question.
If you skip the stoichiometric multiplier, you would incorrectly assume [OH–] = 0.0046 M. That wrong value would produce a pOH of about 2.34 and a pH near 11.66. The correct pH is higher because the actual hydroxide concentration is double that amount. This is exactly why balanced dissociation equations matter in acid-base chemistry.
Quick comparison with common strong bases
| Base | Hydroxide ions released per formula unit | If base concentration is 0.0046 M, then [OH–] | Resulting pOH | Resulting pH at 25 C |
|---|---|---|---|---|
| NaOH | 1 | 0.0046 M | 2.337 | 11.663 |
| KOH | 1 | 0.0046 M | 2.337 | 11.663 |
| Ba(OH)2 | 2 | 0.0092 M | 2.036 | 11.964 |
| Ca(OH)2 | 2 | 0.0092 M | 2.036 | 11.964 |
The chemistry behind the answer
Barium hydroxide is commonly classified as a strong base for equilibrium problems at the introductory level. In a typical classroom pH problem, that means you do not set up a Kb expression or solve for partial ionization. Instead, you assume complete dissociation and calculate hydroxide concentration directly from stoichiometry. This is very similar to how hydrochloric acid, nitric acid, sodium hydroxide, and potassium hydroxide are handled in foundational chemistry coursework.
Once hydroxide concentration is known, the pOH is found from the definition:
pOH = -log[OH–]
And at 25 C:
pH + pOH = 14.00
These equations come from the ionic product of water, Kw. Under standard textbook conditions, Kw is taken as 1.0 × 10-14, giving the well-known relationship between pH and pOH. More advanced courses discuss how Kw changes with temperature, but for a problem stated simply as “calculate the pH of 0.0046 M Ba(OH)2,” the default assumption is almost always 25 C.
Worked example in full
- Given: 0.0046 M Ba(OH)2
- Dissociation: Ba(OH)2 → Ba2+ + 2OH–
- Hydroxide concentration: 2 × 0.0046 = 0.0092 M
- pOH: -log(0.0092) = 2.036212…
- pH: 14.000 – 2.036212… = 11.963788…
- Rounded answer: pH = 11.96
Common mistakes when solving this problem
Even though this is a straightforward strong-base problem, several errors show up repeatedly in homework, quizzes, and exam settings. Knowing them in advance can help you avoid losing easy points.
- Forgetting the two hydroxides. This is the biggest issue. Ba(OH)2 contributes twice as much OH– as a same-molar NaOH solution.
- Using pH = -log(base concentration). pH is based on hydronium concentration, not directly on the base molarity.
- Calculating pOH from 0.0046 instead of 0.0092. This gives a lower pH than the correct answer.
- Mixing up pH and pOH. For a base solution, pOH is the direct logarithmic quantity from [OH–], then pH is found from 14 – pOH.
- Rounding too early. It is better to keep extra digits during intermediate steps and round only at the end.
Error check table
| Approach | [OH–] used | Computed pOH | Computed pH | Status |
|---|---|---|---|---|
| Correct Ba(OH)2 stoichiometry | 0.0092 M | 2.036 | 11.964 | Correct |
| Incorrectly treating Ba(OH)2 like NaOH | 0.0046 M | 2.337 | 11.663 | Incorrect |
| Using pH = -log(0.0046) | Not applicable | Not applicable | 2.337 | Completely incorrect interpretation |
How strong is a pH of about 11.96?
A pH of roughly 11.96 indicates a distinctly basic solution. On the conventional pH scale from 0 to 14 used in introductory chemistry, values above 7 are basic, and values near 12 are strongly alkaline compared with neutral water. This does not necessarily mean the solution is concentrated by industrial standards, but it absolutely means hydroxide ions are present at levels far above those in pure water.
For perspective, pure water at 25 C has [H+] = [OH–] = 1.0 × 10-7 M and a pH of 7.00. Here, the hydroxide concentration is 0.0092 M, which is 9.2 × 10-3 M. Compared with pure water, this is vastly greater than 10-7 M, so the solution is strongly basic.
Relevant data and reference points
General pH scale benchmarks are widely used in chemistry teaching and environmental science. Neutral water is centered at pH 7 at 25 C, while strong bases rise well above that midpoint. Agencies and university chemistry departments often present pH scales showing a logarithmic relationship, meaning each whole pH unit reflects a tenfold change in hydrogen ion activity under simplified instructional treatment.
- Neutral water at 25 C is commonly shown as pH 7.00.
- A solution at pH 11.96 is about 4.96 pH units above neutral.
- Using the standard classroom relationship, that corresponds to a very low hydrogen ion concentration compared with neutral water.
- The hydroxide concentration here, 0.0092 M, is over 90,000 times larger than 1.0 × 10-7 M.
When this simple method works best
This exact approach is appropriate in standard general chemistry problems where the solution concentration is high enough that water autoionization is negligible and the compound is treated as fully dissociated. A concentration of 0.0046 M easily fits that framework. Because the hydroxide concentration from the dissolved base is many orders of magnitude larger than the 1.0 × 10-7 M background level from pure water, the contribution from water itself can be ignored.
In more advanced chemistry, there can be refinements involving activity, ionic strength, temperature dependence of Kw, and detailed solubility or dissociation behavior. But for the specific educational question “calculate the pH of 0.0046 M Ba(OH)2,” the accepted answer is obtained directly and cleanly with strong-base stoichiometry followed by a pOH calculation.
Authority sources for pH and water chemistry
If you want to verify the pH scale, neutral-water assumptions, and related chemistry concepts from authoritative educational and government resources, these references are useful:
- U.S. Geological Survey: pH and Water
- University of Wisconsin Chemistry: Acids, Bases, and pH
- University of Illinois Chemistry: pH and pOH overview
Final answer
For a 0.0046 M Ba(OH)2 solution:
- [OH–] = 0.0092 M
- pOH = 2.036
- pH = 11.964
Rounded to two decimal places, the final pH is 11.96.