Calculate the pH of 0.0048 M Ba(OH)2
Use this premium strong-base calculator to determine the hydroxide concentration, pOH, and final pH for barium hydroxide. The default setup is the exact chemistry problem: 0.0048 M Ba(OH)2 at 25 degrees Celsius.
Calculator Inputs
Assumption: Ba(OH)2 behaves as a strong base and dissociates completely in dilute aqueous solution: Ba(OH)2 → Ba2+ + 2OH–
Result Preview
For 0.0048 M Ba(OH)2, the hydroxide concentration is 0.0096 M, the pOH is 2.0177, and the pH at 25 degrees Celsius is 11.9823.
pH Trend Around the Selected Concentration
How to calculate the pH of 0.0048 M Ba(OH)2
To calculate the pH of 0.0048 M barium hydroxide, you use the fact that Ba(OH)2 is a strong base. In standard general chemistry problems, strong bases are treated as fully dissociated in water. That means every formula unit of barium hydroxide releases one barium ion and two hydroxide ions. This stoichiometric detail is the key to the entire problem.
The dissociation equation is:
Ba(OH)2(aq) → Ba2+(aq) + 2OH–(aq)
Because the initial concentration of Ba(OH)2 is 0.0048 M, the hydroxide concentration is twice that amount:
[OH–] = 2 × 0.0048 = 0.0096 M
Next, calculate pOH using the logarithmic definition:
pOH = -log(0.0096) = 2.0177
At 25 degrees Celsius, the relation between pH and pOH is:
pH + pOH = 14.00
So:
pH = 14.00 – 2.0177 = 11.9823
Step-by-step method explained clearly
Students often know that barium hydroxide is a base, but they sometimes miss the extra stoichiometric factor of 2. If you only use 0.0048 M as the hydroxide concentration, your pH answer will be too low. The correct sequence is straightforward if you separate the chemistry into four clean steps.
- Write the dissociation equation. Ba(OH)2 produces two hydroxide ions for every dissolved unit.
- Convert base concentration to hydroxide concentration. Multiply 0.0048 M by 2 to get 0.0096 M OH–.
- Find pOH. Use pOH = -log[OH–].
- Convert pOH to pH. At 25 degrees Celsius, pH = 14 – pOH.
These four steps work for many strong metal hydroxides. The only part that changes is the number of hydroxide ions released. For example, NaOH releases one OH–, Ca(OH)2 releases two, and Al(OH)3 is more complicated because it is not treated as a simple fully dissociated strong base in the same way under typical aqueous conditions. For the problem here, Ba(OH)2 is usually handled as a strong base in introductory chemistry.
Why barium hydroxide gives twice as much hydroxide
The formula Ba(OH)2 already tells you the ratio. One barium ion has a 2+ charge, and each hydroxide ion has a 1- charge. To balance charge, there must be two hydroxide ions in the compound. When the substance dissociates completely, those two hydroxide ions enter solution and control the solution’s basicity. This is why the hydroxide concentration is not equal to the formal Ba(OH)2 concentration. It is double.
Exact calculation for 0.0048 M Ba(OH)2
- Given concentration of Ba(OH)2 = 0.0048 M
- Hydroxide stoichiometric factor = 2
- [OH–] = 2 × 0.0048 = 0.0096 M
- pOH = -log(0.0096) = 2.0177
- pH = 14.0000 – 2.0177 = 11.9823
Common mistakes when solving this pH problem
Even though this is a standard strong-base problem, a few recurring errors show up again and again in homework, quizzes, and online discussions. Knowing them can save time and points.
- Forgetting the coefficient 2. This is the biggest error. Ba(OH)2 does not produce one hydroxide ion; it produces two.
- Using pH = -log[OH–]. That formula gives pOH, not pH.
- Subtracting in the wrong direction. At 25 degrees Celsius, pH = 14 – pOH, not pOH – 14.
- Ignoring temperature assumptions. The common pH + pOH = 14 relation is exact only at 25 degrees Celsius in introductory settings. At other temperatures, pKw changes.
- Rounding too early. If you round [OH–] or pOH too aggressively, your final pH may drift slightly.
Comparison table: strong base stoichiometry at the same formal concentration
The table below shows why formula stoichiometry matters. Each example uses the same formal concentration, 0.0048 M, but the number of hydroxide ions released changes the hydroxide concentration and therefore the pH. These are direct calculated values at 25 degrees Celsius.
| Base model | OH– released per formula unit | Formal concentration (M) | [OH–] (M) | pOH | pH at 25 degrees Celsius |
|---|---|---|---|---|---|
| NaOH-type | 1 | 0.0048 | 0.0048 | 2.3188 | 11.6812 |
| Ba(OH)2-type | 2 | 0.0048 | 0.0096 | 2.0177 | 11.9823 |
| Hypothetical tri-hydroxide model | 3 | 0.0048 | 0.0144 | 1.8416 | 12.1584 |
This comparison highlights a powerful lesson: pH depends on the actual hydrogen or hydroxide ion concentration, not just the labeled molarity of the compound. For ionic hydroxides, stoichiometric dissociation directly controls that concentration.
Reference data table: pH values for different Ba(OH)2 concentrations
The next table gives realistic computed values for several barium hydroxide concentrations, assuming complete dissociation and 25 degrees Celsius. This helps you see how pH shifts as concentration changes by factors of two or more.
| Ba(OH)2 concentration (M) | [OH–] (M) | pOH | pH |
|---|---|---|---|
| 0.0010 | 0.0020 | 2.6990 | 11.3010 |
| 0.0024 | 0.0048 | 2.3188 | 11.6812 |
| 0.0048 | 0.0096 | 2.0177 | 11.9823 |
| 0.0096 | 0.0192 | 1.7167 | 12.2833 |
| 0.0200 | 0.0400 | 1.3979 | 12.6021 |
Why the answer is basic but not near pH 14
A pH of 11.98 is clearly basic, but it is not an extremely concentrated hydroxide solution. Pure strong bases at very high concentrations can produce pH values approaching 14 in elementary calculations, but 0.0048 M is still a fairly dilute concentration. Because pH is logarithmic, every tenfold change in hydroxide concentration shifts pOH by 1 unit, which shifts pH by 1 unit at 25 degrees Celsius.
That means a small-looking decimal concentration can still be strongly basic, but not necessarily at the very top of the scale. In this problem, the solution contains 0.0096 moles of OH– per liter, which is enough to push the pH to almost 12.
How temperature affects the pH calculation
In many classroom settings, you are expected to use pH + pOH = 14.00. That is appropriate for 25 degrees Celsius. However, advanced chemistry recognizes that the ion-product constant of water changes with temperature. As a result, the pKw value changes too. If you perform the same hydroxide calculation at a different temperature, the pOH from the logarithm of hydroxide concentration stays the same, but the pH conversion may shift slightly because pKw changes.
This is why the calculator above includes a temperature selector. It lets you see how the same solution would map to a slightly different pH when the pKw assumption changes. For most introductory exercises, though, use 25 degrees Celsius unless the problem explicitly says otherwise.
Practical interpretation of the result
A solution with pH near 12 is strongly basic and should be handled with care in a laboratory setting. Barium hydroxide is corrosive, and soluble barium compounds can also pose toxicity concerns. The pH value itself tells you the solution strongly favors hydroxide ions over hydronium ions. In practical terms, such a solution can irritate skin, damage eyes, and react with acids readily.
If you are connecting classroom chemistry with real water chemistry, environmental measurements, or lab safety, it helps to understand that pH is more than just a homework number. Agencies and educational institutions publish extensive guidance on the pH scale, water chemistry, and safe chemical handling. Helpful background resources include the U.S. Geological Survey overview of pH and water, the U.S. Environmental Protection Agency discussion of pH in aquatic systems, and the National Library of Medicine toxicology reference for barium compounds.
Fast mental check for exam situations
If you need a quick exam-time estimate, you can mentally check the answer without a calculator:
- Double 0.0048 to get roughly 0.01 M hydroxide.
- If [OH–] is about 10-2, then pOH is about 2.
- If pOH is about 2, pH is about 12.
Since 0.0096 M is just a little less than 0.0100 M, the pOH should be just a little more than 2, and the pH should be just a little less than 12. That logic confirms the exact result of 11.9823 is sensible.
Final answer summary
Here is the complete solution in compact form:
- Ba(OH)2 is a strong base.
- Each mole of Ba(OH)2 releases 2 moles of OH–.
- [OH–] = 2 × 0.0048 = 0.0096 M
- pOH = -log(0.0096) = 2.0177
- pH = 14.00 – 2.0177 = 11.9823
Therefore, the pH of 0.0048 M Ba(OH)2 is 11.98 to two decimal places, or 11.9823 to four decimal places.