Calculate the pH of a 2 M C2H5NH2 Solution
Use this premium weak-base calculator to find the pH, pOH, hydroxide concentration, conjugate acid concentration, and percent ionization for an ethylamine solution. The calculator uses the exact quadratic solution by default, which is the preferred method for a concentrated weak base such as 2.0 M C2H5NH2.
How to calculate the pH of a 2 M C2H5NH2 solution
To calculate the pH of a 2 M C2H5NH2 solution, you treat ethylamine as a weak Brønsted base. In water, ethylamine accepts a proton from water and forms its conjugate acid, C2H5NH3+, while generating hydroxide ions, OH-. Because pH is directly tied to hydrogen ion activity and, for basic solutions, is most easily reached through pOH, the real target of the equilibrium calculation is the hydroxide concentration at equilibrium.
The key equilibrium is:
The base dissociation constant expression is:
If the initial concentration of ethylamine is 2.00 M and the commonly used Kb is approximately 5.6 × 10-4 at 25°C, then an ICE table gives:
Change: -x, +x, +x
Equilibrium: [C2H5NH2] = 2.00 – x, [C2H5NH3+] = x, [OH-] = x
Substitute those equilibrium values into the Kb expression:
For high accuracy, solve the quadratic equation rather than assuming x is negligible. The exact solution is:
Using Kb = 0.00056 and C = 2.00 M, the hydroxide concentration comes out to about 0.0332 M. Then:
pH = 14.000 – 1.479 ≈ 12.521
So the pH of a 2 M C2H5NH2 solution is approximately 12.52 at 25°C when Kb = 5.6 × 10-4 and pKw = 14.00 are used. Depending on the source you consult for Kb, you may see a slightly different final pH, often by a few hundredths of a pH unit. That small variation is normal because reference tables do not always report the same equilibrium constant.
Why ethylamine gives a basic pH
Ethylamine is an amine, and amines are basic because the nitrogen atom has a lone pair of electrons that can accept a proton. When dissolved in water, only a fraction of the ethylamine molecules react. That is why ethylamine is classified as a weak base rather than a strong base. Even so, a 2.0 M solution is quite concentrated, so the amount of hydroxide produced is still large enough to push the pH well above 12.
There are two ideas students often confuse:
- Weak base does not mean low pH increase. It means incomplete reaction with water.
- Concentrated weak base can still produce a strongly basic solution because there are many moles of base present.
- Ethylamine is more basic than ammonia in water, so at equal concentration it generally gives a slightly higher pH than NH3.
Step by step method using an ICE table
- Write the base hydrolysis equation: C2H5NH2 + H2O ⇌ C2H5NH3+ + OH-.
- Write the Kb expression: Kb = [C2H5NH3+][OH-] / [C2H5NH2].
- Set up the ICE table with initial concentration 2.00 M for ethylamine and zero for products.
- Let x be the amount ionized. Then equilibrium concentrations are 2.00 – x, x, and x.
- Substitute into the Kb expression to get x² / (2.00 – x) = 5.6 × 10-4.
- Solve for x exactly with the quadratic formula or approximately with x = √(KbC) if the approximation is justified.
- Interpret x as [OH-].
- Calculate pOH = -log[OH-].
- Calculate pH = 14.00 – pOH, or more generally pH = pKw – pOH.
Exact method versus approximation
For many classroom weak acid and weak base problems, the approximation x << C works well. In that case, 2.00 – x is replaced with 2.00 and the equation simplifies to x = √(KbC). For ethylamine at 2.00 M, this approximation is actually still fairly good because the fraction ionized is only around 1.66%. However, an exact quadratic solution is better practice when building a reliable calculator because it remains accurate over a much wider range of concentrations and Kb values.
| Method | Formula Used | [OH-] for 2.00 M C2H5NH2, Kb = 5.6 × 10^-4 | Calculated pH | Comment |
|---|---|---|---|---|
| Exact quadratic | x = (-Kb + √(Kb² + 4KbC)) / 2 | 0.03318 M | 12.521 | Best all around method for calculator accuracy |
| Approximation | x = √(KbC) | 0.03347 M | 12.525 | Very close here because ionization is small |
| Difference | Approximation error | 0.00029 M | 0.004 pH units | Small, but exact is preferable |
Important constants and what they mean
The two constants that matter most are Kb and pKw. The Kb value tells you how strongly ethylamine acts as a base in water. A larger Kb means a larger equilibrium [OH-] and therefore a higher pH. The pKw value is the sum of pH and pOH at the chosen temperature. At 25°C, pKw is usually taken as 14.00. If the temperature changes significantly, pKw also changes, so a more advanced calculation would use the proper temperature dependent value.
- Kb for ethylamine: often reported near 5.6 × 10-4, though some references may list values in a nearby range.
- pKb: about 3.25 when Kb = 5.6 × 10-4.
- Conjugate acid pKa: around 10.75, since pKa + pKb = 14.00 at 25°C.
- pKw: commonly 14.00 at 25°C.
Comparison table: ethylamine versus ammonia at the same concentration
One useful way to understand the result is to compare ethylamine with ammonia. Ethylamine is a somewhat stronger weak base than NH3, so it creates a higher hydroxide concentration at the same starting molarity. The table below uses exact quadratic calculations at 25°C.
| Base | Kb | Initial Concentration | Exact [OH-] | pH | Percent Ionization |
|---|---|---|---|---|---|
| Ethylamine, C2H5NH2 | 5.6 × 10^-4 | 2.00 M | 0.03318 M | 12.521 | 1.659% |
| Ammonia, NH3 | 1.8 × 10^-5 | 2.00 M | 0.00599 M | 11.777 | 0.300% |
| Difference | Ethylamine is about 31 times larger in Kb | Same concentration | About 5.5 times larger [OH-] | About 0.744 pH units higher | Much greater ionization |
Common mistakes when calculating the pH of 2 M C2H5NH2
1. Treating ethylamine like a strong base
Some learners see a high molarity and incorrectly assume [OH-] = 2.00 M. That would only be true for a strong Arrhenius base delivering one OH- per formula unit, such as a fully dissociated alkali hydroxide. Ethylamine does not fully ionize, so [OH-] must be found from equilibrium.
2. Confusing Kb with Ka
Ethylamine is a base, not an acid. You should use Kb directly unless the problem provides only the Ka of the conjugate acid, C2H5NH3+. In that case, use Kb = Kw / Ka.
3. Forgetting to convert from pOH to pH
Once you find [OH-], your first logarithmic result is pOH, not pH. Many students stop one step too early. Always apply pH = pKw – pOH.
4. Rounding too early
If you round [OH-] aggressively before taking the logarithm, you can shift the final pH by noticeable hundredths. In chemistry calculations, carry several guard digits through the intermediate steps and round only at the end.
5. Using an approximation without checking it
The approximation x << C is acceptable only when x is small relative to the starting concentration. A common rule is that x/C should be less than 5%. For 2.00 M ethylamine, it is about 1.66%, so the approximation is fine. Even so, a calculator should still be able to solve the exact equation.
What the percent ionization tells you
Percent ionization is a powerful interpretation tool. It is calculated as:
For 2.00 M ethylamine:
That means only about 1.66% of the ethylamine molecules react with water at equilibrium. This is exactly why it is called a weak base. Yet because the starting concentration is so high, 1.66% of 2.00 M still corresponds to a fairly large hydroxide concentration.
How concentration changes the pH of ethylamine
If you lower the concentration of C2H5NH2, the pH drops because the equilibrium produces less hydroxide in absolute terms. However, the percent ionization tends to increase as the solution becomes more dilute. This is a classic pattern in weak acid and weak base chemistry. The balance between concentration and extent of ionization is one reason logarithmic pH scales can feel unintuitive at first.
At the same Kb, a 0.10 M ethylamine solution will have a lower pH than a 2.00 M solution, but a larger fraction of molecules may ionize. This distinction often appears on exams and in laboratory report discussions.
When activity effects start to matter
At 2.00 M, the solution is concentrated enough that a very advanced treatment might consider non-ideal behavior and activity coefficients. Introductory and most general chemistry courses do not require that correction, and textbook pH calculations for weak bases almost always use molarity directly. Still, if you are doing upper level physical chemistry or analytical chemistry, it is worth noting that the thermodynamic activity of each species can differ from its formal concentration in concentrated solutions. That can slightly alter the true pH from the idealized classroom result.
Authoritative chemistry and pH references
USGS: pH and Water
U.S. EPA: pH Overview
University of Washington Department of Chemistry
Final answer
If you use Kb = 5.6 × 10-4 for ethylamine and pKw = 14.00 at 25°C, the pH of a 2 M C2H5NH2 solution is approximately 12.52. The corresponding values are:
- [OH-] ≈ 0.03318 M
- pOH ≈ 1.479
- [C2H5NH3+] ≈ 0.03318 M
- [C2H5NH2] remaining ≈ 1.96682 M
- Percent ionization ≈ 1.659%
That result is the one produced by the calculator above when you keep the default values. If your instructor, lab manual, or problem set provides a different Kb for ethylamine, simply substitute that value and the calculator will update the answer accordingly.