Calculate the pH of a 0.24 M Ba(OH)2 Solution
Use this premium calculator to find hydroxide concentration, pOH, and pH for barium hydroxide solutions. The default example is 0.24 M Ba(OH)2, a strong base that dissociates into one Ba2+ ion and two OH– ions.
Enter the molar concentration of barium hydroxide.
Choose molarity or millimolar.
Ba(OH)2 contributes two hydroxide ions when fully dissociated.
Control output precision for pOH and pH.
This calculator uses the standard relation pH + pOH = 14.00 at 25 C and assumes complete dissociation for a strong base.
Results
Click Calculate pH to see the worked answer for a 0.24 M Ba(OH)2 solution.
How to calculate the pH of a 0.24 M Ba(OH)2 solution
If you need to calculate the pH of a 0.24 M Ba(OH)2 solution, the key idea is that barium hydroxide is treated as a strong base in introductory and general chemistry. That means it dissociates essentially completely in water under the standard classroom assumption. Each formula unit of Ba(OH)2 produces one barium ion, Ba2+, and two hydroxide ions, OH–. Those hydroxide ions determine the pOH and, from there, the pH.
Final answer first
This result comes from multiplying the barium hydroxide concentration by 2, because every mole of Ba(OH)2 yields two moles of hydroxide ion.
Step by step method
Here is the standard procedure that chemistry students and instructors use.
- Write the dissociation equation for barium hydroxide.
- Determine the hydroxide ion concentration from the stoichiometry.
- Calculate pOH using the base 10 logarithm.
- Convert pOH to pH using the 25 C relationship.
1. Write the dissociation equation
Ba(OH)2(aq) → Ba2+(aq) + 2OH-(aq)This equation tells you immediately that one mole of dissolved barium hydroxide gives two moles of hydroxide ion.
2. Find the hydroxide ion concentration
[OH-] = 2 × [Ba(OH)2] [OH-] = 2 × 0.24 = 0.48 MThat means the concentration of hydroxide ion in the final solution is 0.48 M.
3. Calculate the pOH
pOH = -log10[OH-] pOH = -log10(0.48) ≈ 0.3188Rounded to three decimal places, the pOH is 0.319.
4. Convert pOH to pH
pH + pOH = 14.00 pH = 14.00 – 0.3188 = 13.6812Rounded to three decimal places, the pH is 13.681.
Why Ba(OH)2 changes pH so strongly
Barium hydroxide is a strong base because it generates a high concentration of OH– ions in water. The pH scale is logarithmic, not linear. That means each whole number shift in pH represents a tenfold change in hydrogen ion activity. A solution with pH 13.68 is therefore strongly basic. In practical terms, even a moderately concentrated strong base pushes the pH close to the upper end of the common 0 to 14 teaching scale.
It is also important to notice that 0.24 M Ba(OH)2 does not mean 0.24 M OH–. Because the compound contains two hydroxide groups, the hydroxide concentration is doubled. This is one of the most common mistakes made by students when solving strong base pH problems involving Group 2 hydroxides such as Ca(OH)2, Sr(OH)2, and Ba(OH)2.
Common mistakes when solving this problem
- Forgetting the coefficient 2: Ba(OH)2 releases two hydroxide ions, so [OH–] is twice the molarity of Ba(OH)2.
- Using pH = -log[OH-]: That formula gives pOH, not pH.
- Skipping the pOH step: In standard general chemistry, you usually calculate pOH first, then convert to pH.
- Mixing units: If the concentration is given in mM, convert to M before using logarithms unless your calculator handles the conversion directly.
- Ignoring the 25 C assumption: The simple rule pH + pOH = 14.00 is standard at 25 C. At other temperatures, the ion product of water changes.
Worked comparison table for strong bases
The table below shows how stoichiometry changes hydroxide concentration and pH for several strong base examples at 25 C. These are calculation based values using complete dissociation assumptions commonly taught in chemistry courses.
| Base | Formal concentration | OH- factor | [OH-] produced | pOH | pH |
|---|---|---|---|---|---|
| NaOH | 0.24 M | 1 | 0.24 M | 0.620 | 13.380 |
| KOH | 0.10 M | 1 | 0.10 M | 1.000 | 13.000 |
| Ca(OH)2 | 0.12 M | 2 | 0.24 M | 0.620 | 13.380 |
| Ba(OH)2 | 0.24 M | 2 | 0.48 M | 0.319 | 13.681 |
This table makes the main point very clear: compounds with more than one hydroxide ion per formula unit can generate a much larger hydroxide concentration than a one to one strong base at the same formal molarity.
Detailed explanation of the logarithm step
Students often understand the stoichiometry but feel less comfortable with the logarithm. Here is why the pOH expression works:
pOH = -log10[OH-]If the hydroxide concentration is 0.48 M, then log10(0.48) is negative because 0.48 is less than 1. Taking the negative sign of that value gives a small positive pOH. Since the pOH is very low, the pH must be very high. This matches the chemistry, because 0.48 M hydroxide is a concentrated basic solution.
In fact, a useful intuition is that when [OH–] gets close to 1 M, the pOH approaches 0. A pOH near zero means the pH approaches 14 at 25 C. That is exactly the direction we see here with Ba(OH)2.
Comparison table: how dilution changes the pH of Ba(OH)2
The next table shows what happens when the concentration of barium hydroxide changes. These values are useful for checking whether your calculator output makes sense.
| Ba(OH)2 concentration | [OH-] | pOH | pH at 25 C | Interpretation |
|---|---|---|---|---|
| 0.001 M | 0.002 M | 2.699 | 11.301 | Clearly basic but much less concentrated |
| 0.010 M | 0.020 M | 1.699 | 12.301 | Strongly basic |
| 0.100 M | 0.200 M | 0.699 | 13.301 | Very strong base |
| 0.240 M | 0.480 M | 0.319 | 13.681 | Extremely basic under ideal assumptions |
Notice the pattern. Every tenfold dilution increases the pOH by about 1 unit and lowers the pH by about 1 unit, as long as the strong base model remains appropriate and the 25 C assumption is used.
When this standard answer is appropriate
The result of pH = 13.681 is the standard answer expected in most high school chemistry, AP Chemistry, and introductory college chemistry settings. It is appropriate when you assume:
- Ba(OH)2 behaves as a strong electrolyte.
- Dissociation is effectively complete.
- Activities are approximated by concentrations.
- The solution temperature is 25 C.
In more advanced physical chemistry or analytical chemistry, very concentrated ionic solutions can deviate from ideal behavior, and activity corrections may be applied. However, for standard pH calculations in coursework, the direct concentration method is the accepted approach.
Shortcut method for this exact problem
If you want to solve this problem quickly on an exam, use this compact workflow:
- Double the given molarity: 0.24 M becomes 0.48 M OH–.
- Take the negative log: pOH = -log(0.48) = 0.319.
- Subtract from 14: pH = 13.681.
That is the entire calculation.
Safety and real world context
A solution with a pH near 13.68 is highly caustic. Strongly basic solutions can damage skin, eyes, and many materials. While this page focuses on chemical calculation rather than lab handling, it is worth understanding that high pH values correspond to serious reactivity and safety concerns. In practical settings, always follow institutional safety rules, wear proper protective equipment, and use approved waste disposal procedures.
For broader background on pH, water chemistry, and chemical science fundamentals, you can consult these authoritative references:
Bottom line
To calculate the pH of a 0.24 M Ba(OH)2 solution, first recognize that barium hydroxide contributes two hydroxide ions per formula unit. Multiply the formal concentration by 2 to get [OH–] = 0.48 M. Then calculate pOH = -log(0.48) = 0.319. Finally, convert to pH using pH = 14.00 – 0.319 = 13.681 at 25 C. If you remember the stoichiometric factor of 2, this problem becomes fast and straightforward.
Educational note: this calculator is designed for standard chemistry instruction and uses ideal strong base assumptions.