Calculate the pH of a 0.2 M C2H5NH2 Solution
Instantly solve the pH of ethylamine in water using the exact weak-base equilibrium equation, with clear step-by-step output and a live concentration vs pH chart.
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Ready to solveDefault values are set for a 0.2 M ethylamine solution with Kb = 5.6 × 10-4.
Expert Guide: How to Calculate the pH of a 0.2 M C2H5NH2 Solution
Calculating the pH of a 0.2 M C2H5NH2 solution is a classic weak-base equilibrium problem. C2H5NH2 is ethylamine, a simple amine that behaves as a Brønsted-Lowry base in water. Because it accepts a proton from water, it generates hydroxide ions, which make the solution basic. That means the pH will be greater than 7.
If you are solving a homework question that asks for the pH of a .2 m C2H5NH2 solution, your instructor almost always expects you to treat the concentration as 0.20 M unless the course is specifically emphasizing molality. In dilute aqueous chemistry, this is a standard assumption and gives the accepted textbook method.
Step 1: Write the equilibrium reaction
Ethylamine reacts with water according to the weak-base equilibrium:
In this reaction:
- C2H5NH2 is the weak base.
- H2O is the proton donor.
- C2H5NH3+ is the conjugate acid.
- OH- is the hydroxide ion that controls the pH.
The base dissociation constant for ethylamine at 25 C is commonly reported around Kb = 5.6 × 10-4. Slightly different textbooks may list a value close to this, but it will not change the answer very much.
Step 2: Set up the Kb expression
For a weak base, the equilibrium expression is:
Start with an initial concentration of 0.20 M ethylamine. Before reaction, there is essentially no C2H5NH3+ or OH- from the base itself. Let x be the amount that reacts:
- Initial: [C2H5NH2] = 0.20, [C2H5NH3+] = 0, [OH-] = 0
- Change: [C2H5NH2] = -x, [C2H5NH3+] = +x, [OH-] = +x
- Equilibrium: [C2H5NH2] = 0.20 – x, [C2H5NH3+] = x, [OH-] = x
Substitute into the equilibrium expression:
Step 3: Solve for x, which equals [OH-]
There are two standard ways to solve this.
- Approximation method: if x is small compared with 0.20, then 0.20 – x ≈ 0.20.
- Exact method: solve the quadratic equation directly.
Using the approximation:
So the hydroxide concentration is approximately [OH-] = 0.01058 M.
Using the exact quadratic solution:
Substituting Kb = 5.6 × 10-4 and C = 0.20 gives:
This is slightly lower than the approximation, which is exactly what we expect because the approximation ignores the small decrease in base concentration.
Step 4: Convert [OH-] to pOH and pH
Once you know the hydroxide concentration, calculate pOH:
Using the exact value:
Then use the 25 C relationship:
So:
The final answer for the pH of a 0.2 M ethylamine solution is therefore about 12.0. If you use the approximation method, you usually get a pH of about 12.02, which is also acceptable in many classroom settings.
Why the solution is basic
Many students understand the math but want a clearer chemical reason. Ethylamine has a lone pair on nitrogen. That lone pair can accept a proton from water, so water transfers H+ to the amine. This reaction leaves behind OH-. Because hydroxide concentration rises, the pH goes up. The stronger the base, or the higher the concentration, the more hydroxide forms.
Ethylamine is stronger as a base than ammonia because the ethyl group donates electron density toward the nitrogen. That makes the nitrogen lone pair more available for protonation. As a result, ethylamine has a higher Kb than ammonia, and an equally concentrated ethylamine solution will typically have a slightly higher pH than ammonia.
Common student mistakes
- Using Ka instead of Kb. Ethylamine is a base, so use Kb unless you are solving through the conjugate acid.
- Forgetting to calculate pOH first. Weak bases produce OH-, not H3O+ directly.
- Assuming the base fully dissociates. Ethylamine is weak, so it does not behave like NaOH.
- Dropping the exact solution too early. The square-root method is usually close, but not always appropriate at low concentrations or with larger Kb values.
- Confusing 0.2 m with 0.2 M. In introductory problems, this notation is often used loosely, but formal solution chemistry normally uses molarity for pH calculations.
Data table: weak-base strength comparison
The table below compares several common weak bases. These values show why ethylamine gives a noticeably basic solution. A larger Kb means the base forms more OH- at the same starting concentration.
| Base | Formula | Kb at 25 C | pKb | Relative basicity comment |
|---|---|---|---|---|
| Ammonia | NH3 | 1.8 × 10^-5 | 4.74 | Much weaker than ethylamine |
| Methylamine | CH3NH2 | 4.4 × 10^-4 | 3.36 | Strong weak base, similar to simple alkyl amines |
| Ethylamine | C2H5NH2 | 5.6 × 10^-4 | 3.25 | Stronger than ammonia and slightly stronger than methylamine in many tables |
| Aniline | C6H5NH2 | 4.3 × 10^-10 | 9.37 | Very weak because the lone pair is delocalized into the ring |
This comparison helps you build intuition. Ethylamine is not a strong base, but it is a much stronger weak base than ammonia. That is why a 0.20 M solution lands around pH 12 instead of somewhere closer to neutral.
Data table: pH of ethylamine at different concentrations
The next table uses the exact equilibrium method with Kb = 5.6 × 10-4. It shows how concentration changes the pH of C2H5NH2 solutions.
| Initial concentration (M) | Exact [OH-] at equilibrium (M) | pOH | pH |
|---|---|---|---|
| 0.010 | 0.00210 | 2.68 | 11.32 |
| 0.050 | 0.00502 | 2.30 | 11.70 |
| 0.100 | 0.00721 | 2.14 | 11.86 |
| 0.200 | 0.01031 | 1.99 | 12.01 |
| 0.500 | 0.01646 | 1.78 | 12.22 |
| 1.000 | 0.02339 | 1.63 | 12.37 |
Notice that pH rises as concentration increases, but it does not rise in a perfectly linear way. That is because weak-base equilibria depend on both the concentration and the equilibrium constant.
Approximation vs exact solution
In many textbook problems, the approximation x << C works well when the percent ionization stays small. For the 0.20 M ethylamine example, the exact solution gives x ≈ 0.01031 M, so the percent ionization is:
That is just a bit above the common 5% classroom guideline, which means the approximation is borderline but still very close. This is why many answer keys accept both 12.01 and 12.02, depending on the method used and rounding policy.
If you want the most defensible chemistry answer, use the exact quadratic equation. If you want speed on a test and your instructor allows approximations, the square-root method usually gives a perfectly reasonable estimate.
When to be careful with notation
The phrase calculate the pH of a .2 m C2H5NH2 solution contains a typo and an ambiguity. In chemistry, lowercase m formally means molality, while uppercase M means molarity. Strictly speaking, pH calculations are typically based on molarity because equilibrium expressions use concentrations. In introductory chemistry, however, many informal problem statements use m and M loosely, especially online. If the solvent is water and the solution is relatively dilute, treating 0.2 m as about 0.2 M usually gives the expected result.
Authoritative references for pH and acid-base chemistry
If you want to study the broader theory behind weak-base calculations and pH, these references are useful starting points:
Final answer
For a 0.20 M C2H5NH2 solution at 25 C using Kb = 5.6 × 10-4, the exact weak-base equilibrium calculation gives:
If your class uses the square-root approximation, you will get essentially the same classroom answer: pH ≈ 12.02. Either way, the important conclusion is the same: ethylamine forms a distinctly basic solution in water.