Calculate pH of 0.1000 M Ethylamine
Use this premium calculator to determine the pH, pOH, hydroxide concentration, and percent ionization for aqueous ethylamine, a weak base. The default setup is preloaded for 0.1000 M ethylamine at 25 degrees Celsius using a typical Kb value of 5.6 × 10-4.
Calculated Results
How to Calculate the pH of 0.1000 M Ethylamine
If you need to calculate the pH of 0.1000 M ethylamine, the key idea is that ethylamine is a weak base, not a strong base. That means it does not fully dissociate in water. Instead, it reacts only partially with water to produce hydroxide ions, and the equilibrium amount of hydroxide determines the pH. This distinction matters because the correct solution is not simply pH based on 0.1000 M OH-. You must use an equilibrium expression involving the weak base constant, Kb.
Ethylamine, often written as C2H5NH2, belongs to the amine family. Amines contain a nitrogen atom with a lone pair, which lets them accept protons from water. In water, ethylamine behaves according to the equilibrium:
C2H5NH2 + H2O ⇌ C2H5NH3+ + OH–
This equilibrium shows why the solution becomes basic. The base pulls a proton from water and generates OH–. Once you know the hydroxide concentration at equilibrium, you can find pOH and then pH. For a standard problem using 0.1000 M ethylamine at 25 degrees Celsius, a typical Kb value is 5.6 × 10-4. Using that constant, the pH is about 11.86 when solved accurately.
Step by Step Setup for the Ethylamine pH Problem
To solve the problem systematically, define the initial concentration of ethylamine as C = 0.1000 M and let x represent the amount that reacts with water. Then the equilibrium concentrations are:
- [C2H5NH2] = 0.1000 – x
- [C2H5NH3+] = x
- [OH–] = x
The weak base expression is:
Kb = [C2H5NH3+][OH–] / [C2H5NH2]
Substitute the ICE table values:
5.6 × 10-4 = x² / (0.1000 – x)
At this point, many chemistry students use the weak base approximation and assume x is small compared with 0.1000. That gives x² / 0.1000 ≈ 5.6 × 10-4, so x ≈ √(5.6 × 10-5) ≈ 0.00748 M. This is close, but the more rigorous exact solution uses the quadratic formula because x is not tiny relative to 0.1000.
Exact Quadratic Calculation
Starting from:
5.6 × 10-4 = x² / (0.1000 – x)
Multiply both sides:
5.6 × 10-4(0.1000 – x) = x²
5.6 × 10-5 – 5.6 × 10-4x = x²
Rearrange into quadratic form:
x² + 5.6 × 10-4x – 5.6 × 10-5 = 0
Using the positive root of the quadratic formula, you obtain:
x = [OH–] ≈ 0.007215 M
Then compute:
- pOH = -log(0.007215) ≈ 2.1416
- pH = 14.0000 – 2.1416 ≈ 11.8584
That is the best answer for the standard problem. If your textbook uses a slightly different Kb for ethylamine, your final pH may vary by a few hundredths of a pH unit. That does not mean your method is wrong. It simply reflects the fact that equilibrium constants are tabulated with some source to source variation.
- Concentration of ethylamine = 0.1000 M
- Typical Kb = 5.6 × 10-4
- Equilibrium [OH–] ≈ 7.215 × 10-3 M
- pOH ≈ 2.1416
- pH ≈ 11.8584
Why Ethylamine Is More Basic Than Ammonia
Students often compare ethylamine with ammonia because both are nitrogen bases. Ethylamine is generally more basic in water because the ethyl group donates electron density toward nitrogen. That makes the lone pair more available to accept a proton. As a result, ethylamine has a larger Kb than ammonia and gives a higher pH at the same formal concentration. This is one reason 0.1000 M ethylamine has a noticeably stronger basic character than 0.1000 M ammonia.
| Weak base | Typical Kb at 25 degrees Celsius | Relative basic strength | Comments |
|---|---|---|---|
| Ammonia, NH3 | 1.8 × 10-5 | Lower than ethylamine | Common benchmark weak base in general chemistry |
| Methylamine, CH3NH2 | 4.4 × 10-4 | Comparable, slightly lower | Alkyl substitution increases basicity versus ammonia |
| Ethylamine, C2H5NH2 | 5.6 × 10-4 | Moderately strong weak base | Typical value used in textbook pH problems |
| Dimethylamine, (CH3)2NH | 5.4 × 10-4 | Very similar to ethylamine | Steric and solvation effects influence exact ranking |
| Pyridine, C5H5N | 1.7 × 10-9 | Much weaker | Aromatic nitrogen base with far lower proton affinity in water |
Approximation vs Exact Method
Should you use the square root approximation or the quadratic formula? The answer depends on how large x is compared with the initial concentration. A common classroom guideline is the 5 percent rule. If x is less than 5 percent of the starting concentration, the approximation is typically acceptable. For 0.1000 M ethylamine, the exact x value is about 0.007215 M, which is roughly 7.2 percent of 0.1000 M. That means the 5 percent rule is not satisfied, so the exact method is preferred.
Even so, the approximation is still educationally useful because it provides a quick estimate. The approximate pH comes out near 11.87, while the exact answer is about 11.86. The difference is small in this case, but if your instructor specifically asks whether the approximation is valid, the correct response is that it is somewhat marginal and the quadratic solution is more defensible.
| Ethylamine concentration | Exact [OH-] using Kb = 5.6 × 10-4 | Calculated pH | Percent ionization |
|---|---|---|---|
| 0.0100 M | 2.094 × 10-3 M | 11.321 | 20.94% |
| 0.0500 M | 5.022 × 10-3 M | 11.701 | 10.04% |
| 0.1000 M | 7.215 × 10-3 M | 11.858 | 7.215% |
| 0.2500 M | 1.156 × 10-2 M | 12.063 | 4.625% |
| 0.5000 M | 1.646 × 10-2 M | 12.216 | 3.293% |
Interpretation of the Concentration Trend
The data table above shows a classic weak base trend. As formal concentration increases, pH rises, but percent ionization drops. That happens because equilibrium shifts in a way that causes a smaller fraction of the base to react at higher concentrations. This is a very common pattern for weak acids and weak bases. It also helps explain why the approximation becomes better at larger concentrations: x becomes a smaller fraction of the initial concentration.
Common Mistakes When Solving the pH of Ethylamine
- Treating ethylamine like a strong base. You cannot assume [OH-] = 0.1000 M.
- Using Ka instead of Kb. Ethylamine is a base, so Kb is the direct starting constant.
- Forgetting to convert from pOH to pH. In basic solution, you usually find pOH first, then pH = 14 – pOH at 25 degrees Celsius.
- Applying the approximation automatically. Always test whether x is small enough relative to the initial concentration.
- Rounding too early. Keep extra digits during intermediate steps, especially when using logarithms.
When a Different Kb Value Changes the Answer
Different tables may list slightly different Kb values for ethylamine, such as 4.3 × 10-4, 5.4 × 10-4, or 5.6 × 10-4, depending on source, ionic strength assumptions, and textbook conventions. Because pH depends logarithmically on hydroxide concentration, these differences usually shift the final pH only modestly. Still, for graded work, use the exact value provided by your class materials whenever possible.
If you are entering your own Kb into the calculator above, you can immediately see how the final pH changes. That is especially helpful for lab reports or homework systems that use a different database from your textbook.
Useful Chemistry Context for Exams and Labs
Knowing how to calculate the pH of 0.1000 M ethylamine is useful far beyond one homework problem. Weak base calculations appear throughout general chemistry, analytical chemistry, biochemistry, environmental chemistry, and industrial formulations. Amines are common in organic and biological systems, so understanding their proton accepting behavior is important for predicting solution properties, extraction behavior, and buffer performance.
In a lab setting, ethylamine solutions may be relevant when discussing:
- Acid base titrations of weak bases
- Conjugate acid and conjugate base relationships
- Buffer regions for amine and ammonium systems
- How alkyl substituents affect electron donation and basicity
- Why ionic strength and temperature can shift equilibrium values slightly
Quick Problem Solving Checklist
- Write the base reaction with water.
- Set up an ICE table.
- Insert concentrations into the Kb expression.
- Solve for x, either approximately or exactly.
- Interpret x as [OH-].
- Calculate pOH.
- Convert pOH to pH.
- Check whether the result is chemically reasonable for a weak base.
Authoritative Reference Links
For readers who want source material on ethylamine, acid base concepts, and chemical properties, these references are useful starting points:
- NIH PubChem entry for ethylamine
- Purdue University acid base review
- Michigan State University acid base fundamentals
Bottom Line
To calculate the pH of 0.1000 M ethylamine, treat ethylamine as a weak base and use the Kb expression rather than assuming full dissociation. With a typical Kb of 5.6 × 10-4, the exact equilibrium solution gives [OH-] ≈ 0.007215 M, pOH ≈ 2.1416, and pH ≈ 11.8584. That result fits the chemistry perfectly: ethylamine is definitely basic, but not so strong that its hydroxide concentration equals its starting concentration. If you remember that one distinction, weak base problems like this become much easier and much more intuitive.