Calculate the pH and pOH of 0.0092 M Ba(OH)2
Use this premium strong-base calculator to solve the pH and pOH for barium hydroxide solutions. The default setup is already configured for 0.0092 M Ba(OH)2, and you can adjust the stoichiometric hydroxide count or temperature assumption if needed.
pH and pOH visualization
How to calculate the pH and pOH of 0.0092 M Ba(OH)2
If you need to calculate the pH and pOH of 0.0092 M Ba(OH)2, the key idea is that barium hydroxide is a strong base that dissociates essentially completely in introductory chemistry problems. That means the chemistry is more about stoichiometry and logarithms than about solving an equilibrium table. Once you know how many hydroxide ions are produced per formula unit and how to use the pOH relationship, the answer becomes straightforward and very repeatable.
The exact problem asks for the pH and pOH of a 0.0092 molar solution of barium hydroxide, written as Ba(OH)2. Since this compound contains two hydroxide groups, every mole of dissolved Ba(OH)2 produces two moles of OH– under the standard strong-base assumption. That is the single detail students most often miss. If you use 0.0092 M directly as the hydroxide concentration, your pOH and pH will be off.
[OH–] = 2 × 0.0092 = 0.0184 M
pOH = -log(0.0184) = 1.735
pH = 14.00 – 1.735 = 12.265
The final answer
Using the standard 25 C textbook assumption where pH + pOH = 14.00, the values for a 0.0092 M solution of barium hydroxide are:
Depending on your instructor or textbook, you may round pOH to 1.74 and pH to 12.26 or 12.27. Since the original concentration 0.0092 M has two significant figures, many chemistry classes would report the final logarithmic values to two decimal places:
- pOH ≈ 1.74
- pH ≈ 12.26
Step by step method
1. Write the dissociation equation
Barium hydroxide is a metal hydroxide and behaves as a strong base in water. In the simplified general chemistry model, it dissociates completely:
Ba(OH)2 → Ba2+ + 2OH–
This equation tells you that one mole of Ba(OH)2 generates two moles of hydroxide ions. The stoichiometric coefficient of 2 is what drives the rest of the problem.
2. Convert base molarity into hydroxide molarity
The solution concentration is 0.0092 M Ba(OH)2. Because there are two hydroxide ions per unit of dissolved base:
- Start with 0.0092 M Ba(OH)2
- Multiply by 2 for the two OH– ions
- Get [OH–] = 0.0184 M
[OH–] = 2 × 0.0092 = 0.0184 M
3. Calculate pOH
The pOH scale is defined using the negative base-10 logarithm of hydroxide concentration:
pOH = -log[OH–]
Substitute the hydroxide concentration:
pOH = -log(0.0184) = 1.735
Since 0.0184 is less than 1, its logarithm is negative, so the negative sign in front converts the final pOH into a positive value.
4. Calculate pH
At 25 C, the standard relationship is:
pH + pOH = 14.00
Therefore:
pH = 14.00 – 1.735 = 12.265
Because the pH is well above 7, the solution is strongly basic, which is exactly what you expect for a soluble hydroxide salt such as barium hydroxide.
Why Ba(OH)2 must be treated differently from NaOH
Students often solve sodium hydroxide problems correctly but make mistakes when they switch to compounds like calcium hydroxide or barium hydroxide. The reason is simple. Sodium hydroxide, NaOH, contributes one hydroxide ion per formula unit. Barium hydroxide, Ba(OH)2, contributes two. If two solutions have the same formal molarity, the barium hydroxide solution produces twice the hydroxide concentration and therefore has a lower pOH and higher pH.
- 1.0 mole NaOH gives 1.0 mole OH–
- 1.0 mole Ba(OH)2 gives 2.0 moles OH–
- Higher [OH–] means stronger basic character on the pH scale
This stoichiometric thinking is central to acid-base chemistry. Before using pH or pOH equations, always ask how many H+ or OH– ions are actually generated by the compound in solution.
Common mistake check for this exact question
Here are the most frequent errors seen in the problem “calculate the pH and pOH of 0.0092 M Ba(OH)2“:
- Forgetting the coefficient 2. Using 0.0092 M directly for [OH–] gives the wrong answer.
- Using pH = -log(0.0092). That formula is for hydronium concentration, not hydroxide concentration in a strong base problem.
- Mixing pH and pOH definitions. For bases, it is usually easiest to find pOH first from [OH–], then convert to pH.
- Rounding too early. Keep extra digits through the logarithm step and round only at the end.
- Ignoring temperature assumptions. The relationship pH + pOH = 14.00 is specifically the common 25 C approximation.
Comparison table: strong base examples at the same formal concentration
The table below compares several strong bases at the same initial molarity of 0.0092 M under the 25 C textbook model. It shows how hydroxide stoichiometry changes pOH and pH.
| Base | Formal concentration (M) | OH– ions per unit | [OH–] (M) | pOH | pH |
|---|---|---|---|---|---|
| NaOH | 0.0092 | 1 | 0.0092 | 2.036 | 11.964 |
| KOH | 0.0092 | 1 | 0.0092 | 2.036 | 11.964 |
| Ca(OH)2 | 0.0092 | 2 | 0.0184 | 1.735 | 12.265 |
| Ba(OH)2 | 0.0092 | 2 | 0.0184 | 1.735 | 12.265 |
The data make the pattern clear. Holding formal concentration constant, bases with two hydroxide ions per formula unit generate more OH–, so their pOH decreases and their pH increases.
Temperature matters: pKw is not always 14.00
In most homework settings, instructors expect you to use 25 C and pKw = 14.00. Still, it is scientifically important to know that the ionic product of water changes with temperature. That means the sum pH + pOH is not fixed at 14.00 under all conditions.
| Temperature | Approximate pKw | Formula used | pOH for [OH–] = 0.0184 M | Resulting pH |
|---|---|---|---|---|
| 0 C | 14.94 | pH = 14.94 – pOH | 1.735 | 13.205 |
| 20 C | 14.17 | pH = 14.17 – pOH | 1.735 | 12.435 |
| 25 C | 14.00 | pH = 14.00 – pOH | 1.735 | 12.265 |
| 50 C | 13.26 | pH = 13.26 – pOH | 1.735 | 11.525 |
These values are useful comparison data because they show that pH is temperature-dependent even when the hydroxide concentration is unchanged. For introductory problems, though, 25 C remains the standard unless a different temperature is explicitly given.
Detailed reasoning behind the logarithm step
The p-scale is logarithmic, not linear. That means a change of one pH unit corresponds to a tenfold change in hydrogen ion concentration. The same principle applies to pOH and hydroxide concentration. Because of this, doubling or halving concentration does not cause a simple additive change in pH. Instead, the logarithm compresses a large concentration range into the familiar 0 to 14 style scale.
For this problem, [OH–] = 0.0184 M can also be written as 1.84 × 10-2. Taking the logarithm:
log(1.84 × 10-2) = log(1.84) + log(10-2)
= 0.2648 – 2 = -1.7352
Applying the negative sign from the pOH definition gives:
pOH = 1.7352
This expanded view helps students understand why the answer is around 1.7 rather than around 0.02 or 18.4. The logarithm translates concentration into a manageable scale.
Practical interpretation of the result
A pH of about 12.26 to 12.27 indicates a strongly basic solution. Such a solution is corrosive and should be handled with proper eye and skin protection in a laboratory environment. Barium hydroxide solutions can cause significant irritation and must be treated with appropriate chemical safety protocols. From an educational perspective, this high pH value nicely illustrates the relationship between concentration, stoichiometry, and acid-base strength.
It is also a good reminder that pH values greater than 7 indicate basic conditions, but not all bases are equally basic at the same molarity. The number of hydroxide ions released per dissolved unit matters enormously. That is why 0.0092 M Ba(OH)2 ends up more basic than 0.0092 M NaOH.
Short summary you can use on homework
If you need a concise write-up, you can use the following structure:
- Ba(OH)2 is a strong base and dissociates completely.
- Each mole gives 2 moles of OH–.
- [OH–] = 2(0.0092) = 0.0184 M.
- pOH = -log(0.0184) = 1.74.
- pH = 14.00 – 1.74 = 12.26.
That answer is compact, chemically correct, and aligned with standard general chemistry expectations.
Authoritative references for pH, water chemistry, and alkalinity
If you want to read more about pH, hydroxide chemistry, and water quality fundamentals, these sources are useful starting points: