Calculate the pH of a 5.0 × 10-3 M KOH Solution
Use this premium calculator to find hydroxide concentration, pOH, and pH for a potassium hydroxide solution. For the standard problem, a 5.0 × 10-3 M KOH solution at 25°C gives a pH of 11.70.
Ready to calculate. Default values are set to the target example: 5.0 × 10-3 M KOH at 25°C.
Expert Guide: How to Calculate the pH of a 5.0 × 10-3 M KOH Solution
Calculating the pH of a 5.0 × 10-3 M KOH solution is a classic general chemistry problem because it combines three foundational ideas: strong-base dissociation, logarithms, and the relationship between pH and pOH. The short answer is simple: at 25°C, the pH is 11.70. However, understanding why that answer is correct is what helps students solve similar questions quickly and accurately on homework, quizzes, standardized exams, and in laboratory work.
Potassium hydroxide, KOH, is a strong base. In water, it dissociates essentially completely into potassium ions and hydroxide ions. That means if you are given a KOH concentration of 5.0 × 10-3 M, then the hydroxide concentration is also 5.0 × 10-3 M. From there, you calculate pOH with the negative logarithm, and then convert pOH to pH using the water ion-product relationship. This is a direct and elegant example of how chemical stoichiometry and logarithmic scales work together.
Step 1: Recognize that KOH is a strong base
The first conceptual step is identifying the compound. KOH, or potassium hydroxide, belongs to the family of strong metal hydroxides. In introductory chemistry, strong bases are treated as compounds that dissociate completely in water. The dissociation equation is:
KOH(aq) → K+(aq) + OH–(aq)
This tells you something very important: for every 1 mole of KOH that dissolves, you get 1 mole of OH–. Since the stoichiometric ratio is 1:1, the hydroxide ion concentration is the same as the original KOH concentration, assuming complete dissociation and dilute solution behavior.
- KOH is a strong base.
- It dissociates nearly 100% in water under ordinary dilute conditions.
- One formula unit of KOH produces one hydroxide ion.
- Therefore, [OH–] = [KOH].
So for this problem:
[OH–] = 5.0 × 10-3 M
Step 2: Calculate pOH from hydroxide concentration
Once you know the hydroxide ion concentration, the next step is to calculate pOH. The formula is:
pOH = -log[OH–]
Substitute the concentration:
pOH = -log(5.0 × 10-3)
Using logarithm rules, this becomes:
pOH = -[log(5.0) + log(10-3)]
pOH = -[0.6990 – 3.0000] = 2.3010
Rounded properly, the pOH is:
pOH = 2.30
This is a good place to pause and check whether the value is reasonable. A solution with a moderately small hydroxide concentration should have a pOH lower than 7, because it is basic. Since 2.30 is well below 7, the result is consistent with expectations.
Step 3: Convert pOH to pH
At 25°C, the relationship between pH and pOH is:
pH + pOH = 14.00
Now plug in the pOH value:
pH = 14.00 – 2.30 = 11.70
That is the final answer for the standard classroom version of the problem:
The pH of a 5.0 × 10-3 M KOH solution is 11.70.
Worked solution in a compact exam-ready format
- Write the dissociation equation: KOH → K+ + OH–
- Since KOH is a strong base, set [OH–] = 5.0 × 10-3 M.
- Compute pOH: pOH = -log(5.0 × 10-3) = 2.30.
- Compute pH: pH = 14.00 – 2.30 = 11.70.
Why students often make mistakes on this problem
Although this is a straightforward calculation, several common mistakes appear repeatedly:
- Confusing pH with pOH. Some students calculate 2.30 and stop, forgetting that this value is pOH, not pH.
- Forgetting complete dissociation. KOH is a strong base, so there is no weak-base ICE table needed here.
- Misreading scientific notation. 10-3 means 0.001, not 0.01 or 0.0001.
- Using the wrong stoichiometric ratio. KOH produces one OH–, unlike Ba(OH)2, which produces two hydroxides per formula unit.
- Ignoring temperature assumptions. The relation pH + pOH = 14.00 is exact only at 25°C in standard introductory chemistry treatment.
Comparison table: KOH concentration vs pOH and pH at 25°C
The following values are based on complete dissociation and the standard 25°C relation pH + pOH = 14.00. This table helps you see where 5.0 × 10-3 M fits within a wider concentration range.
| KOH concentration (M) | [OH–] (M) | pOH | pH | Basicity level |
|---|---|---|---|---|
| 1.0 × 10-1 | 1.0 × 10-1 | 1.00 | 13.00 | Very strongly basic |
| 1.0 × 10-2 | 1.0 × 10-2 | 2.00 | 12.00 | Strongly basic |
| 5.0 × 10-3 | 5.0 × 10-3 | 2.30 | 11.70 | Strongly basic |
| 1.0 × 10-3 | 1.0 × 10-3 | 3.00 | 11.00 | Basic |
| 1.0 × 10-4 | 1.0 × 10-4 | 4.00 | 10.00 | Basic |
Comparison table: Common strong bases and hydroxide yield
This second table highlights why stoichiometry matters. The pH calculation method depends not only on molarity but also on how many hydroxide ions each formula unit releases.
| Base | Formula | Hydroxides released per formula unit | Molar mass (g/mol) | Calculation note |
|---|---|---|---|---|
| Potassium hydroxide | KOH | 1 | 56.11 | [OH–] = base molarity |
| Sodium hydroxide | NaOH | 1 | 40.00 | [OH–] = base molarity |
| Lithium hydroxide | LiOH | 1 | 23.95 | [OH–] = base molarity |
| Barium hydroxide | Ba(OH)2 | 2 | 171.34 | [OH–] = 2 × base molarity |
How significant figures affect the answer
The concentration is written as 5.0 × 10-3 M, which has two significant figures in the coefficient 5.0. When reporting logarithmic results such as pH and pOH, the number of decimal places in the pH should match the number of significant figures in the concentration term. Since 5.0 has two significant figures, the pOH and pH are appropriately reported with two digits after the decimal point:
- pOH = 2.30
- pH = 11.70
This is a subtle but important chemistry convention. A calculator may show more digits, but the properly reported value should match the precision implied by the measurement.
What changes if temperature changes?
Many introductory chemistry problems assume 25°C, where pKw = 14.00. But in more advanced settings, the sum pH + pOH changes with temperature because the autoionization constant of water changes. This is why the calculator above includes optional temperature assumptions. At 25°C, the standard textbook approach is correct and expected. If the problem does not specify temperature, 25°C is almost always the intended assumption.
For rigorous background on pH in water systems, consult the USGS Water Science School overview of pH and water and the EPA page on pH in aquatic systems. For academic reinforcement of acid-base equilibrium methods, a university-level resource such as Purdue University chemistry guidance on acid-base equilibria is also useful.
When would this easy method not be enough?
The direct method works perfectly for this problem because KOH is a strong base and the concentration is high enough that hydroxide from water autoionization is negligible. There are cases, however, where more care is needed:
- Extremely dilute strong base solutions can require accounting for water autoionization.
- Weak bases like NH3 require an equilibrium expression and Kb.
- Buffers require Henderson-Hasselbalch or equilibrium methods.
- Polyhydroxide bases such as Ba(OH)2 require stoichiometric adjustment before taking the logarithm.
For the present problem, none of those complications apply. The strong-base shortcut is fully appropriate.
Fast mental estimation method
If you want to estimate the answer quickly without a full calculator workflow, use this logic:
- 5.0 × 10-3 M KOH gives 5.0 × 10-3 M OH–.
- 10-3 corresponds to a pOH near 3.
- Because the coefficient is 5.0, the pOH is a bit less than 3, specifically 2.30.
- Subtract from 14 to get pH near 11.70.
This estimation technique is especially helpful on timed tests, since it lets you catch arithmetic errors immediately.
Frequently asked question: Why is the pH above 7?
A solution with excess hydroxide ions is basic, and basic solutions have pH values greater than 7 at 25°C. Because KOH releases OH– directly and completely, even a millimolar-range concentration drives the pH significantly above neutral. In this case, the hydroxide concentration is 0.0050 M, which is much larger than the 1.0 × 10-7 M hydroxide concentration associated with neutral water at 25°C.
Summary of the full chemistry logic
To calculate the pH of a 5.0 × 10-3 M KOH solution, first identify KOH as a strong base. Because it dissociates completely, the hydroxide concentration is the same as the KOH concentration: 5.0 × 10-3 M. Next, calculate pOH using pOH = -log[OH–], which gives 2.30. Finally, use pH = 14.00 – 2.30 = 11.70 at 25°C. That is the standard, correct, textbook answer.