pH Calculator for 0.68 M KC7H5O2
Use this premium calculator to determine the pH of a potassium benzoate solution, KC7H5O2. The tool applies salt hydrolysis, converts the conjugate-acid Ka to Kb, estimates hydroxide concentration, and returns pOH and pH with a visual chart.
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Enter or keep the default values, then click Calculate pH.
Method Summary
KC7H5O2 is potassium benzoate, the salt of KOH and benzoic acid. Potassium is a spectator ion, while benzoate undergoes hydrolysis:
- Find Kb from the conjugate relationship: Kb = Kw / Ka.
- For a weak base salt at moderate concentration, estimate hydroxide by [OH-] ≈ √(Kb × C).
- Then compute pOH = -log10[OH-].
- Finally, pH = 14 – pOH.
How to calculate the pH of 0.68 M KC7H5O2
If you need to calculate the pH of 0.68 M KC7H5O2, you are really solving a classic salt hydrolysis problem from acid-base chemistry. KC7H5O2 is potassium benzoate, a salt formed from the strong base potassium hydroxide and the weak acid benzoic acid. That combination matters because salts from strong bases and weak acids produce basic aqueous solutions. In other words, when potassium benzoate dissolves in water, the potassium ion does almost nothing to pH, but the benzoate ion acts as a weak base and generates hydroxide.
The key idea is that the conjugate base of a weak acid reacts with water. Here, benzoate is the conjugate base of benzoic acid. So the chemistry is not based on direct proton donation like an acid problem. Instead, the benzoate ion pulls a proton from water and creates OH-. That OH- is what raises the pH above 7.
Step 1: Identify the ions produced by the salt
Potassium benzoate dissociates essentially completely in water:
The potassium ion, K+, comes from a strong base and is effectively neutral in water. The benzoate ion, C7H5O2-, is the species that matters. Because it is the conjugate base of benzoic acid, it hydrolyzes according to the equilibrium:
Step 2: Use Ka of benzoic acid to find Kb of benzoate
Most textbook and lab references list the acid dissociation constant of benzoic acid rather than the base dissociation constant of benzoate. A common value at 25 C is:
The relationship between conjugate pairs is:
Using Kw = 1.0 × 10-14 at 25 C:
Step 3: Set up the weak-base hydrolysis expression
The initial concentration of benzoate equals the formal concentration of the salt, so for 0.68 M KC7H5O2:
Let x represent the hydroxide concentration produced by hydrolysis. Then:
Because Kb is extremely small and 0.68 M is relatively large, x will be tiny compared with 0.68. That allows the standard weak-base approximation:
Substitute the numbers:
So:
Step 4: Convert hydroxide concentration to pOH and pH
Now calculate pOH:
Then use the standard relation at 25 C:
Final answer: the pH of 0.68 M KC7H5O2 is approximately 9.02 at 25 C when Ka for benzoic acid is taken as 6.3 × 10-5.
Why the solution is basic
Many students memorize categories such as “salt of strong acid and strong base is neutral” or “salt of weak acid and strong base is basic,” but it helps to understand why. The potassium ion has essentially no tendency to react with water because it is derived from a strong base. Benzoate, however, is stable enough to exist in solution yet still basic enough to accept a proton from water. That proton transfer creates OH-, which drives the pH upward.
In practical terms, the strength of the basic behavior depends on how weak the parent acid is. Benzoic acid is weak, but not extremely weak. Its conjugate base is therefore weakly basic, which is why the pH rises to only around 9 rather than 11 or 12.
What if your instructor uses a slightly different Ka?
Different textbooks round acid dissociation constants differently. Some may use 6.25 × 10-5, 6.3 × 10-5, or 6.46 × 10-5 for benzoic acid. That changes the final pH slightly, usually by only a few hundredths. So an answer near 9.0 is generally correct unless your course requires a specific constant and temperature.
| Benzoic Acid Ka Used | Calculated Kb of Benzoate | Estimated [OH-] at 0.68 M | pH at 25 C |
|---|---|---|---|
| 6.25 × 10^-5 | 1.60 × 10^-10 | 1.04 × 10^-5 M | 9.019 |
| 6.30 × 10^-5 | 1.59 × 10^-10 | 1.04 × 10^-5 M | 9.017 |
| 6.46 × 10^-5 | 1.55 × 10^-10 | 1.03 × 10^-5 M | 9.011 |
Full worked solution in ICE-table logic
If you prefer a formal equilibrium setup, the hydrolysis reaction can be treated with an ICE table.
- Initial: 0.68, 0, 0
- Change: -x, +x, +x
- Equilibrium: 0.68 – x, x, x
Substitute into the expression for Kb:
Since x is much smaller than 0.68, simplify to:
That gives the same hydroxide concentration and the same pH. The 5% rule is easily satisfied because x / 0.68 is tiny.
Common mistakes to avoid
- Using Ka directly to calculate H+. Benzoate is a base, so you must convert Ka to Kb first.
- Forgetting that K+ is neutral. Potassium does not meaningfully affect pH here.
- Using the wrong concentration. The benzoate concentration equals the salt concentration because the salt dissociates strongly.
- Confusing benzoic acid with benzene derivatives that are not acids. The relevant parent acid is benzoic acid, HC7H5O2.
- Ignoring temperature. The common pH = 14 – pOH relation assumes Kw = 1.0 × 10-14 at 25 C.
How concentration affects the pH of potassium benzoate
For weak base salts like KC7H5O2, increasing concentration increases hydroxide concentration, but not in a one-to-one way. Because the approximation depends on the square root of concentration, a 100-fold increase in concentration raises [OH-] by about 10-fold, which changes pOH by 1 unit and pH by about 1 unit at 25 C. This is why concentrated weak base salts are only moderately basic compared with strong bases.
| KC7H5O2 Concentration | Approximate [OH-] | Approximate pOH | Approximate pH |
|---|---|---|---|
| 0.010 M | 1.26 × 10^-6 M | 5.90 | 8.10 |
| 0.050 M | 2.82 × 10^-6 M | 5.55 | 8.45 |
| 0.100 M | 3.99 × 10^-6 M | 5.40 | 8.60 |
| 0.680 M | 1.04 × 10^-5 M | 4.98 | 9.02 |
| 1.000 M | 1.26 × 10^-5 M | 4.90 | 9.10 |
Comparison with other salt types
This problem becomes much easier once you classify the salt correctly. Here is the logic chemists use:
- Strong acid + strong base salt: generally neutral, pH near 7.
- Weak acid + strong base salt: basic, as in KC7H5O2.
- Strong acid + weak base salt: acidic.
- Weak acid + weak base salt: depends on the relative values of Ka and Kb.
Because benzoic acid is weak and potassium hydroxide is strong, potassium benzoate lands squarely in the “basic salt” category.
Practical relevance of pH and hydrolysis
Acid-base calculations like this appear in general chemistry, analytical chemistry, pharmaceutical formulation, food preservation, and environmental chemistry. Benzoate salts are particularly relevant because benzoic acid and related benzoates are widely discussed in preservation chemistry and equilibrium speciation. In laboratory settings, understanding pH from weak acid conjugate bases is also essential for preparing buffers and interpreting titration curves.
For broader reference on pH and acid-base principles, consult authoritative educational and government resources such as the U.S. Environmental Protection Agency pH overview, the University of Wisconsin discussion of basic salts, and Purdue University acid-base equilibrium materials.
Final takeaway
To calculate the pH of 0.68 M KC7H5O2, treat the benzoate ion as a weak base, not as an acid. Convert the known Ka of benzoic acid into Kb, use the hydrolysis approximation to estimate hydroxide concentration, and then convert to pOH and pH. With Ka = 6.3 × 10-5 and Kw = 1.0 × 10-14, the solution gives pH ≈ 9.02 at 25 C.
That single number is important, but the more valuable lesson is the chemical reasoning behind it: salts of strong bases and weak acids make basic solutions because their anions hydrolyze in water to produce OH-. Once that concept is clear, this entire class of pH problems becomes much easier to solve accurately and quickly.