Calculate pH for Strong Base Solution 8.7 × 10-2 M KOH
Use this premium calculator to determine hydroxide concentration, pOH, and pH for a strong base such as potassium hydroxide at 25°C. It is preloaded for the common chemistry example of 8.7 × 10-2 M KOH, but you can change the values to explore any strong base concentration.
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Enter your values and click Calculate pH to see the full worked answer.
Expert Guide: How to Calculate pH for a Strong Base Solution 8.7 × 10-2 M KOH
When students search for how to calculate pH for strong base solution 8.7 10 2m KOH, they are usually referring to the chemistry expression 8.7 × 10-2 M KOH. Written in standard decimal form, that concentration is 0.087 M potassium hydroxide. Because KOH is a strong base, it dissociates essentially completely in water, which makes the pH calculation much more direct than it would be for a weak base. The entire process depends on converting concentration into hydroxide ion concentration, finding pOH, and then converting pOH into pH.
Strong base calculations are foundational in general chemistry, analytical chemistry, and laboratory work because they illustrate how concentration directly controls alkalinity. Potassium hydroxide is a classic example because it is highly soluble and behaves ideally in introductory chemistry problems. In a textbook setting, if the solution is dilute enough to remain physically reasonable and the temperature is assumed to be 25°C, you can use the standard relationship pH + pOH = 14. This calculator and guide follow that standard convention.
Step 1: Interpret the concentration correctly
The notation 8.7 × 10-2 M means 8.7 multiplied by 0.01. So the molarity is:
- 8.7 × 10-2 = 0.087
- Therefore, the KOH concentration is 0.087 M
This means there are 0.087 moles of KOH dissolved per liter of solution. Since KOH is a strong base, each mole of KOH produces one mole of OH- ions in water:
KOH → K+ + OH-
That one-to-one stoichiometric relationship is why the hydroxide concentration equals the base concentration for KOH.
Step 2: Determine hydroxide ion concentration
For KOH, the dissociation factor is 1 because one formula unit releases one hydroxide ion. Therefore:
- [OH-] = 0.087 M
If the base had been Ca(OH)2 or Ba(OH)2, you would multiply the molarity by 2 because each formula unit releases two hydroxide ions. But for potassium hydroxide, the calculation stays simple.
Step 3: Calculate pOH
The pOH equation is:
pOH = -log10[OH-]
Substitute the hydroxide concentration:
pOH = -log10(0.087)
Using a calculator:
pOH ≈ 1.060
This value tells you the basic strength on the hydroxide scale. Lower pOH means a more strongly basic solution.
Step 4: Convert pOH to pH
At 25°C, aqueous solutions follow:
pH + pOH = 14
So:
pH = 14 – 1.060 = 12.940
The final answer is:
Why KOH is treated as a strong base
Potassium hydroxide belongs to the class of strong Arrhenius bases, substances that produce hydroxide ions almost completely when dissolved in water. In introductory and intermediate chemistry, KOH is assumed to dissociate 100% for routine pH problems. This assumption is why you do not need an equilibrium constant expression such as Kb when solving the problem. By contrast, weak bases like ammonia require ICE tables, equilibrium reasoning, and often approximations.
Because KOH dissociates completely, pH is governed directly by stoichiometry. That makes these problems ideal for learning the difference between strong electrolytes and weak electrolytes. When concentration increases, [OH-] increases proportionally, which pushes pOH downward and raises pH further above neutral.
Worked example in compact form
- Given: 8.7 × 10-2 M KOH
- Convert to decimal: 0.087 M KOH
- Because KOH is a strong base: [OH-] = 0.087 M
- Calculate pOH: pOH = -log(0.087) ≈ 1.060
- Calculate pH: 14 – 1.060 = 12.940
That is the standard method your chemistry teacher, textbook, or lab manual expects unless the problem states a different temperature or asks for activity corrections at higher ionic strengths.
Comparison table: Strong base examples at 25°C
| Base | Formal Concentration (M) | OH- Released per Formula Unit | [OH-] (M) | pOH | pH |
|---|---|---|---|---|---|
| KOH | 8.7 × 10-2 | 1 | 0.087 | 1.060 | 12.940 |
| NaOH | 1.0 × 10-2 | 1 | 0.010 | 2.000 | 12.000 |
| LiOH | 5.0 × 10-3 | 1 | 0.0050 | 2.301 | 11.699 |
| Ca(OH)2 | 2.0 × 10-2 | 2 | 0.040 | 1.398 | 12.602 |
Real laboratory perspective on pH values
In practical laboratory chemistry, pH values for strong bases can differ slightly from simple textbook calculations because real solutions may depart from ideality. At relatively high ionic strengths, the effective concentration of ions, called activity, may be lower than the formal molarity. For most classroom problems, however, activity corrections are not required. The expected answer for 0.087 M KOH remains about 12.94.
Another factor is temperature. The familiar rule pH + pOH = 14 is valid at 25°C because it depends on the ionic product of water at that temperature. If temperature changes significantly, the exact sum differs. Most general chemistry assignments explicitly or implicitly assume 25°C unless otherwise stated. This calculator uses that convention to match standard educational practice.
Comparison table: Concentration vs pH for KOH at 25°C
| KOH Concentration (M) | [OH-] (M) | pOH | pH | Interpretation |
|---|---|---|---|---|
| 1.0 × 10-4 | 0.0001 | 4.000 | 10.000 | Mildly basic |
| 1.0 × 10-3 | 0.001 | 3.000 | 11.000 | Clearly basic |
| 1.0 × 10-2 | 0.01 | 2.000 | 12.000 | Strongly basic |
| 8.7 × 10-2 | 0.087 | 1.060 | 12.940 | Very strongly basic |
| 1.0 × 10-1 | 0.10 | 1.000 | 13.000 | Very strongly basic |
Common mistakes to avoid
- Dropping the negative exponent incorrectly: 8.7 × 10-2 is 0.087, not 0.0087 and not 8.7.
- Using pH instead of pOH first: for strong bases, calculate pOH from [OH-], then convert to pH.
- Forgetting stoichiometry: KOH gives one OH-, but Ca(OH)2 gives two.
- Using natural log instead of base-10 log: pH and pOH use log base 10.
- Ignoring temperature assumptions: pH + pOH = 14 is the standard only at 25°C.
When this simple method works best
This direct method is appropriate when the base is strong, the concentration is provided, and the problem does not request activity corrections or nonstandard temperature treatment. It works especially well for compounds such as KOH, NaOH, LiOH, and soluble group 2 hydroxides when their stoichiometric OH- contribution is accounted for. It is exactly the method used in most homework problems, quizzes, placement exams, and introductory laboratory calculations.
Why the result is chemically reasonable
A pH of 12.94 indicates a highly basic solution, which is consistent with 0.087 M KOH. Since neutral water has a pH near 7 at 25°C, this solution contains a much larger hydroxide concentration than pure water. The pOH of about 1.06 also makes sense because a hydroxide concentration near 10-1 M should produce a pOH close to 1. As a quick estimate, 0.087 M is close to 0.1 M, and 0.1 M OH- corresponds to pOH = 1 and pH = 13, so the exact answer 12.94 is right in the expected range.
Authoritative references for pH and aqueous chemistry
For broader background on pH, water chemistry, and standard measurement concepts, review these authoritative sources:
Final takeaway
If you need to calculate pH for strong base solution 8.7 × 10-2 M KOH, the process is straightforward because KOH fully dissociates. Convert the concentration to decimal form, set [OH-] equal to the molarity, compute pOH with the negative logarithm, and subtract from 14. The resulting pH is approximately 12.94 at 25°C. Once you understand this pattern, you can solve almost any strong base pH problem quickly and with confidence.