Calculate pH of a 0.09 M Barium Hydroxide Solution
Use this interactive calculator to find hydroxide concentration, pOH, and pH for barium hydroxide, Ba(OH)2. By default, the calculator assumes complete dissociation in water at 25°C, which is the standard approach for general chemistry pH problems.
Enter the analytical concentration of Ba(OH)2.
How to calculate the pH of a 0.09 M barium hydroxide solution
Barium hydroxide, written as Ba(OH)2, is a strong base. In a standard general chemistry problem, you typically assume that it dissociates completely in water. That means every mole of barium hydroxide produces one mole of barium ions, Ba2+, and two moles of hydroxide ions, OH–. Since pH for bases is found by first determining pOH from the hydroxide concentration, this is a classic multi step stoichiometric pH calculation.
For the specific question, “calculate pH of a 0.09 M barium hydroxide solution,” the most important idea is that the hydroxide concentration is not 0.09 M. It is double that amount because each formula unit contributes two hydroxide ions. Therefore:
If the solution concentration is 0.09 M in Ba(OH)2, then the hydroxide concentration is:
Once you have [OH–], use the pOH formula:
At 25°C, pH and pOH are related by:
So the pH is:
Rounded to two decimal places, the pH of a 0.09 M barium hydroxide solution is 13.26. This confirms that the solution is strongly basic, which is exactly what you would expect from a strong metal hydroxide that releases two hydroxide ions per formula unit.
Step by step method you can reuse
Many students can compute the answer correctly once, but the goal is to build a reusable process. If you understand the structure of the problem, you can solve similar questions for calcium hydroxide, sodium hydroxide, strontium hydroxide, lithium hydroxide, and even weak base systems where an equilibrium setup is needed. For strong hydroxides like barium hydroxide, the following workflow is the fastest and most reliable.
- Write the dissociation equation for the base.
- Determine how many moles of OH– are released per mole of base.
- Multiply the formal concentration of the base by that stoichiometric factor.
- Use pOH = -log[OH–].
- Use pH = 14.00 – pOH at 25°C.
- Round appropriately based on the problem instructions or significant figures.
Worked example for 0.09 M Ba(OH)2
- Given concentration of Ba(OH)2 = 0.09 M
- Dissociation stoichiometry = 2 OH– per 1 Ba(OH)2
- [OH–] = 2 x 0.09 = 0.18 M
- pOH = -log(0.18) = 0.7447
- pH = 14.00 – 0.7447 = 13.2553
- Final answer = 13.26
Why barium hydroxide behaves as a strong base
Strong bases are substances that dissociate essentially completely in dilute aqueous solution. Barium hydroxide belongs to this category in standard introductory chemistry treatment. When dissolved, it releases hydroxide ions that directly determine the basicity of the solution. Because there are two hydroxide ions in each formula unit, Ba(OH)2 can generate more OH– than an equal molar amount of a monohydroxide such as NaOH or KOH.
This stoichiometric doubling matters a lot. A 0.09 M sodium hydroxide solution would have [OH–] = 0.09 M, but a 0.09 M barium hydroxide solution has [OH–] = 0.18 M. That difference changes pOH and shifts pH upward. Since the pH scale is logarithmic, even modest differences in hydroxide concentration can produce meaningful changes in pH.
Comparison of hydroxide release by common strong bases
| Base | Formula | OH- released per mole | If base concentration is 0.09 M, [OH-] | Resulting pH at 25°C |
|---|---|---|---|---|
| Sodium hydroxide | NaOH | 1 | 0.09 M | 12.95 |
| Potassium hydroxide | KOH | 1 | 0.09 M | 12.95 |
| Calcium hydroxide | Ca(OH)2 | 2 | 0.18 M | 13.26 |
| Barium hydroxide | Ba(OH)2 | 2 | 0.18 M | 13.26 |
The table above shows the stoichiometric effect very clearly. At the same formal molarity, dihydroxides produce twice as much hydroxide ion as monohydroxides. Since pOH equals the negative logarithm of hydroxide concentration, that doubling lowers pOH and raises pH.
Detailed explanation of each mathematical step
1. Start with the balanced dissociation equation
Every pH problem involving a strong base begins with chemical identity and stoichiometry. For barium hydroxide:
This tells you that one dissolved formula unit produces two hydroxide ions. The coefficient of 2 in front of OH– is what drives the rest of the calculation.
2. Convert the base concentration to hydroxide concentration
If the solution is 0.09 M in barium hydroxide, then:
This is a direct stoichiometric multiplication. No equilibrium table is required in the usual strong base approximation.
3. Calculate pOH
Now apply the definition:
Because 0.18 is less than 1, its logarithm is negative, and the negative sign in the formula makes pOH positive.
4. Convert pOH to pH
At 25°C, the ion product of water corresponds to the familiar relationship:
Thus:
Rounded appropriately, the final answer is 13.26.
Common mistakes when solving this problem
Even straightforward strong base calculations can go wrong if a student rushes or uses formulas mechanically. Here are the most frequent errors and how to avoid them.
- Using 0.09 M as [OH-]: This ignores that Ba(OH)2 gives 2 OH–.
- Calculating pH directly from base molarity: You must usually calculate pOH from hydroxide concentration first.
- Forgetting the 14.00 relationship: At 25°C, pH = 14.00 – pOH.
- Using natural log instead of base 10 log: pH and pOH use log base 10.
- Rounding too early: Keep more digits in intermediate steps, then round at the end.
Incorrect versus correct setup
| Approach | [OH-] used | pOH | pH | Comment |
|---|---|---|---|---|
| Incorrect: ignores stoichiometry | 0.09 M | 1.0458 | 12.95 | Too low because only one hydroxide was counted |
| Correct: accounts for 2 OH- | 0.18 M | 0.7447 | 13.26 | Matches the balanced equation |
How strong is a pH of 13.26?
A pH of 13.26 is very strongly basic. For context, neutral water at 25°C has a pH near 7. Household baking soda solutions are mildly basic, while a concentrated strong base such as barium hydroxide produces a much higher hydroxide ion concentration and correspondingly much higher pH. In practice, such solutions are corrosive and require proper eye, skin, and lab safety precautions.
The logarithmic nature of pH means a change of one pH unit corresponds to a tenfold change in hydrogen ion activity under simplified textbook conditions. So a pH above 13 indicates an extremely alkaline solution. Even though classroom problems focus on math, the chemical reality is that strong hydroxide solutions can damage tissue and react with certain materials.
Does molarity versus molality matter here?
Your question uses 0.09 M, which means molarity, or moles of solute per liter of solution. In many chemistry problems, molarity is the standard concentration unit for pH calculations because pH is fundamentally tied to concentrations in solution. Sometimes people accidentally write lowercase m for molality. Molality is moles of solute per kilogram of solvent and is used more often in colligative property work. For this calculator and for the typical textbook problem, 0.09 M means 0.09 moles of Ba(OH)2 per liter of solution.
If a problem truly gives molality instead of molarity, then an exact pH calculation would require additional density information to convert accurately between concentration bases. However, that is not the standard interpretation of this problem statement. In most educational settings, “0.09 M barium hydroxide” clearly calls for the strong base stoichiometry method described above.
Real data references and why pH assumptions matter
In introductory chemistry, using pH + pOH = 14.00 is appropriate at 25°C. That relation comes from the temperature dependent autoionization of water. The pH scale and acid base behavior are widely discussed in educational and government sources, including the U.S. Geological Survey and chemistry departments at major universities. If you want to cross check your understanding of pH, hydroxide concentration, and water chemistry, these resources are excellent starting points:
- USGS: pH and Water
- U.S. EPA: pH Overview
- University based chemistry course collections and pH topics
When using sources, keep in mind that environmental pH discussions often involve natural waters, buffering, dissolved gases, and activity effects, while textbook problems like this one usually assume ideal behavior, complete dissociation, and a 25°C reference state. Those simplifications are exactly why the math can be done so cleanly.
Quick reference summary
- Barium hydroxide is a strong base.
- It dissociates as Ba(OH)2 -> Ba2+ + 2OH–.
- A 0.09 M solution gives [OH–] = 0.18 M.
- pOH = -log(0.18) = 0.7447.
- pH = 14.00 – 0.7447 = 13.2553.
- Rounded answer: 13.26.
Final answer
If you need a single concise result, the pH of a 0.09 M barium hydroxide solution is 13.26 at 25°C, assuming complete dissociation and standard textbook treatment of a strong base.