Calculate the pH of a 0.100 M Ethylamine Solution if pKb Is Known
Use this interactive weak-base calculator to determine Kb, equilibrium hydroxide concentration, pOH, and final pH for an aqueous ethylamine solution. It supports exact quadratic and common approximation methods.
Enter molarity in mol/L. Default is 0.100 M.
A commonly used textbook value for ethylamine is near 3.25 to 3.29 at 25 C.
Use the exact method when you want the most rigorous answer.
This calculator uses pH + pOH = 14.00 under the standard 25 C assumption.
Results
Enter your values and click Calculate pH to see the full weak-base equilibrium solution.
How to calculate the pH of a 0.100 M ethylamine solution if pKb is given
To calculate the pH of a 0.100 M ethylamine solution when the pKb is known, you treat ethylamine as a weak base in water. Unlike a strong base such as sodium hydroxide, ethylamine does not ionize completely. Instead, it establishes an equilibrium between unprotonated ethylamine molecules, water, the ethylammonium ion, and hydroxide ions. Because pH depends directly on the concentration of hydroxide formed, the calculation centers on converting pKb into Kb, solving the equilibrium expression, and then converting the resulting hydroxide concentration into pOH and pH.
This is a classic general chemistry problem because it combines equilibrium, logarithms, and acid-base relationships in one neat process. It is also practical. Ethylamine is a real organic base used in synthesis and industrial chemistry, so understanding its aqueous behavior is more than a textbook exercise. In a classroom setting, you will often see the concentration written as 0.100 M and the pKb supplied by the instructor or data table. Once you know the pKb, the rest is systematic.
Step 1: Write the weak-base equilibrium
The first step is always the chemical equation. Ethylamine, C2H5NH2, acts as a Brønsted-Lowry base by accepting a proton from water:
C2H5NH2 + H2O ⇌ C2H5NH3+ + OH–
The important product for pH work is OH–. Once you know the equilibrium hydroxide concentration, you can calculate pOH and then pH.
Step 2: Convert pKb to Kb
The relationship between pKb and Kb is:
Kb = 10-pKb
If the pKb is 3.25, then:
Kb = 10-3.25 = 5.62 x 10-4
This tells you that ethylamine is a weak base, but not an extremely weak one. A Kb on the order of 10-4 means a measurable fraction of the base reacts with water to produce hydroxide.
Step 3: Set up an ICE table
For a 0.100 M starting solution, use an ICE table:
- Initial: [C2H5NH2] = 0.100, [C2H5NH3+] = 0, [OH–] = 0
- Change: -x, +x, +x
- Equilibrium: 0.100 – x, x, x
Now substitute these equilibrium concentrations into the Kb expression:
Kb = [C2H5NH3+][OH–] / [C2H5NH2]
5.62 x 10-4 = x2 / (0.100 – x)
Step 4: Solve for x
In many classroom problems, students use the weak-base approximation and assume that x is small compared with 0.100. Then the denominator becomes approximately 0.100:
5.62 x 10-4 ≈ x2 / 0.100
x2 ≈ 5.62 x 10-5
x ≈ 7.50 x 10-3 M
That means:
- [OH–] ≈ 7.50 x 10-3 M
- [C2H5NH3+] ≈ 7.50 x 10-3 M
- [C2H5NH2] remaining ≈ 0.0925 M
If you want the exact solution, solve the quadratic equation instead. For this concentration and Kb value, the exact answer is very close to the approximation, which is why instructors often allow the simpler method.
Step 5: Convert hydroxide concentration to pOH and pH
Once [OH–] is known, compute pOH:
pOH = -log(7.50 x 10-3) = 2.12
Then use the standard 25 C relationship:
pH = 14.00 – 2.12 = 11.88
So if the pKb of ethylamine is 3.25, the pH of a 0.100 M ethylamine solution is approximately 11.88.
Worked example using exact equilibrium math
It is helpful to verify the same result using the exact quadratic method, especially if you want to understand where the approximation comes from. Starting from:
Kb = x2 / (C – x)
Rearrange:
x2 + Kb x – KbC = 0
With C = 0.100 and Kb = 5.62 x 10-4, the positive root is:
x = [-Kb + sqrt(Kb2 + 4KbC)] / 2
That gives x very near 7.22 x 10-3 M. The pOH becomes about 2.14 and the pH becomes about 11.86. The approximation and exact methods differ only slightly here, so both tell the same chemical story: ethylamine produces a distinctly basic solution.
| Given pKb | Calculated Kb | Approximate [OH-] in 0.100 M solution | Approximate pH at 25 C |
|---|---|---|---|
| 3.20 | 6.31 x 10^-4 | 7.94 x 10^-3 M | 11.90 |
| 3.25 | 5.62 x 10^-4 | 7.50 x 10^-3 M | 11.88 |
| 3.29 | 5.13 x 10^-4 | 7.16 x 10^-3 M | 11.85 |
| 3.35 | 4.47 x 10^-4 | 6.69 x 10^-3 M | 11.83 |
Why ethylamine is basic but not as strong as a strong base
Ethylamine contains a nitrogen atom with a lone pair of electrons. That lone pair allows it to accept a proton, so it behaves as a base. However, because proton transfer from water to ethylamine is only partial, not complete, the hydroxide concentration remains far below the starting analytical concentration of the base. Compare that with sodium hydroxide, where a 0.100 M solution gives about 0.100 M OH– directly. That difference is why strong bases have much higher pH values at the same concentration.
For students, one of the most important conceptual takeaways is this: pKb does not directly tell you the pH. It tells you the equilibrium tendency of the base. The actual pH still depends on concentration. A very dilute solution of the same base would give a noticeably lower pH because less hydroxide would form overall.
Ethylamine compared with other weak bases
Ethylamine is often discussed alongside methylamine, ammonia, and aniline. These compounds differ in basicity because of electronic effects, solvation, and the stability of the protonated form. In introductory chemistry, the main value of comparing them is that it shows how molecular structure affects equilibrium constants.
| Base | Representative pKb at 25 C | Typical Kb | Approximate pH for a 0.100 M solution |
|---|---|---|---|
| Ethylamine | 3.25 to 3.29 | 5.1 x 10^-4 to 5.6 x 10^-4 | 11.85 to 11.88 |
| Methylamine | 3.36 | 4.4 x 10^-4 | About 11.83 |
| Ammonia | 4.75 | 1.8 x 10^-5 | About 11.13 |
| Aniline | 9.40 | 4.0 x 10^-10 | Near neutral to mildly basic |
Common mistakes when solving this problem
- Using pKa instead of pKb. Ethylamine is acting as a base here, so you need the base dissociation constant or pKb.
- Forgetting to convert pKb to Kb. You cannot substitute pKb directly into the equilibrium expression.
- Assuming [OH-] equals 0.100 M. That would only be true for a strong base, not a weak base like ethylamine.
- Mixing up pOH and pH. The equilibrium gives hydroxide, so pOH comes first, then pH.
- Ignoring the validity of the approximation. After using x = sqrt(KbC), check whether x is less than about 5 percent of the initial concentration if your course requires it.
Fast classroom shortcut
If you need a quick answer on an exam and the approximation is valid, use this sequence:
- Convert pKb to Kb
- Use x = sqrt(KbC)
- Set [OH-] = x
- Calculate pOH
- Calculate pH = 14.00 – pOH
For 0.100 M ethylamine with pKb = 3.25, this quickly leads to a pH of about 11.88. That is usually accepted unless your instructor specifically requests the exact quadratic solution.
Authoritative references for acid-base data and pH fundamentals
For readers who want primary or instructional sources, these references are useful:
- U.S. Environmental Protection Agency: What is pH?
- NIST Chemistry WebBook: Ethylamine data
- University of Wisconsin chemistry tutorial on weak acids and bases
Final answer summary
When asked to calculate the pH of a 0.100 M ethylamine solution if pKb is given, the correct approach is to treat ethylamine as a weak base, convert pKb to Kb, solve the base-equilibrium expression, and then use the hydroxide concentration to find pOH and pH. If pKb = 3.25, then Kb = 5.62 x 10^-4. Solving the equilibrium gives a hydroxide concentration around 7.2 x 10^-3 to 7.5 x 10^-3 M, depending on whether you use the exact or approximate method. That leads to a final pH of about 11.86 to 11.88 at 25 C.
In simple terms, a 0.100 M ethylamine solution is clearly basic but not as basic as a strong base of the same concentration. The pKb tells you how strongly ethylamine accepts a proton, and the concentration tells you how much hydroxide can actually build up in solution. Together, those two pieces of information determine the pH.