Calculate pH of a 40 m Solution of Ethylamine
Use this interactive weak-base calculator to estimate the pH, pOH, hydroxide concentration, conjugate-acid concentration, and percent protonation for an ethylamine solution. The default setup is a 40 m solution of ethylamine using a typical literature value of Kb for C2H5NH2.
- Default molality: 40 m
- Ethylamine pKb: 3.25
- Quadratic weak-base solution
- Live chart output
Weak Base Calculator
For the target problem, enter 40 to represent a 40 m ethylamine solution.
Typical ethylamine value: pKb ≈ 3.25, equivalent to Kb ≈ 5.62 × 10-4.
Click “Calculate pH” to solve the equilibrium for ethylamine in water.
Concentration Profile Chart
This chart compares the initial base concentration with the calculated equilibrium concentrations of ethylamine, ethylammonium, and hydroxide ion.
Model used: C2H5NH2 + H2O ⇌ C2H5NH3+ + OH-
At very high concentrations such as 40 m, non-ideal behavior and activity effects can become important. This calculator uses the standard weak-base equilibrium expression as a practical estimate.
Expert Guide: How to Calculate the pH of a 40 m Solution of Ethylamine
To calculate the pH of a 40 m solution of ethylamine, you treat ethylamine as a weak Brønsted base that reacts with water to generate hydroxide ions. Ethylamine, written as C2H5NH2, accepts a proton from water to form its conjugate acid, ethylammonium, C2H5NH3+, while producing OH-. That hydroxide production is what makes the solution basic. In most general chemistry and analytical chemistry settings, the equilibrium is solved from the base dissociation constant, Kb, or from the equivalent pKb value.
The standard reaction is:
For ethylamine, a commonly cited room-temperature value is Kb ≈ 5.6 × 10-4, corresponding to pKb ≈ 3.25. If the solution concentration is given as 40 m, the notation usually means 40 molal, or 40 moles of solute per kilogram of solvent. In many classroom pH calculations, especially when a problem does not provide density or activity coefficients, molality is treated approximately like concentration in the weak-base expression. That approximation is not perfect at very high concentration, but it is the expected textbook workflow unless the problem explicitly requests an activity-based treatment.
Short Answer for the 40 m Ethylamine Problem
Using a standard weak-base equilibrium calculation with C = 40 and Kb = 5.62 × 10-4, the hydroxide concentration is obtained from the quadratic equation:
where x = [OH-] = [C2H5NH3+] at equilibrium. Solving gives:
- x ≈ 0.1497
- pOH ≈ 0.825
- pH ≈ 13.18 at 25°C
So the commonly accepted weak-base estimate for the pH of a 40 m solution of ethylamine is about 13.18.
Step-by-Step Method
- Write the equilibrium reaction. Ethylamine acts as a weak base and reacts with water: C2H5NH2 + H2O ⇌ C2H5NH3+ + OH-
- Set up the ICE table. Start with initial ethylamine concentration C and assume no initial ethylammonium or hydroxide contributed by the base: [C2H5NH2] = 40, [C2H5NH3+] = 0, [OH-] = 0. At equilibrium, these become 40 – x, x, and x.
- Insert into the Kb expression. Kb = [C2H5NH3+][OH-] / [C2H5NH2] = x2 / (40 – x)
- Substitute Kb for ethylamine. 5.62 × 10-4 = x2 / (40 – x)
- Solve the quadratic. Rearranging gives x2 + Kb x – 40Kb = 0. Solving yields x ≈ 0.1497.
- Convert to pOH and pH. pOH = -log(0.1497) ≈ 0.825, then pH = 14.00 – 0.825 = 13.175.
Why the Quadratic Method Is Better Than the Simplified Approximation
Students are often taught to approximate weak-base equilibria using x ≈ √(KbC). That shortcut is useful and, in this case, it gives almost the same answer:
That estimate leads to essentially the same pH, roughly 13.18. Even so, the quadratic method is the more defensible approach because it directly solves the exact equilibrium expression. For high-concentration systems, you want the most controlled algebraic treatment available before worrying about higher-level corrections such as activities and ionic strength effects.
What Makes Ethylamine Basic?
Ethylamine contains a nitrogen atom with a lone pair of electrons. That lone pair can accept a proton, making the molecule a weak base. Compared with ammonia, ethylamine is a somewhat stronger base because the ethyl group donates electron density toward nitrogen. This stabilizes the protonated form and improves proton acceptance. The result is a larger Kb than ammonia and therefore a higher pH at the same formal concentration.
| Base | Formula | Typical Kb at 25°C | Typical pKb | Relative Basicity vs Ammonia |
|---|---|---|---|---|
| Ammonia | NH3 | 1.8 × 10-5 | 4.74 | Reference point |
| Methylamine | CH3NH2 | 4.4 × 10-4 | 3.36 | Stronger |
| Ethylamine | C2H5NH2 | 5.6 × 10-4 | 3.25 | Stronger |
| Dimethylamine | (CH3)2NH | 5.4 × 10-4 | 3.27 | Stronger |
This comparison helps explain why ethylamine solutions are noticeably basic. Since ethylamine has a Kb substantially higher than ammonia, it creates more OH- at equilibrium under similar conditions.
Important Note About 40 m Concentration
A 40 m solution is extremely concentrated. In rigorous physical chemistry, concentration terms in equilibrium expressions should often be replaced by activities, especially when the solution is non-ideal. At such high solute levels, interactions between ions and molecules are significant, and the true pH can differ from the value predicted by the simple weak-base formula. However, most educational chemistry questions that ask you to “calculate the pH of a 40 m solution of ethylamine” are testing whether you know how to apply the Kb equilibrium model. In that context, the expected answer is the textbook value near 13.18.
If the problem came from an advanced thermodynamics or solution chemistry course, you would need more information, such as activity coefficients, density, and perhaps even a non-ideal solvent model. Because none of that is usually supplied in a standard pH problem, the conventional approach remains the correct exam-style solution.
Worked Example with Numbers
Let C = 40 and Kb = 5.62 × 10-4.
- Equation: Kb = x2 / (40 – x)
- Rearranged: x2 + (5.62 × 10-4)x – 0.02248 = 0
- Positive root: x ≈ 0.1497
- [OH-] = 0.1497
- pOH = -log(0.1497) ≈ 0.825
- pH = 14.000 – 0.825 = 13.175
You can also estimate the fraction protonated by dividing x by the initial base concentration:
This result is a great reminder that a weak base can still produce a very high pH even though only a small percentage of molecules actually react with water. The initial concentration is so large that a tiny reacted fraction still creates a significant hydroxide concentration.
How pH Changes as Ethylamine Concentration Changes
One of the most useful ways to understand this system is to see how the pH scales with concentration. As the formal concentration increases, the hydroxide concentration increases, but not linearly, because ethylamine is a weak base governed by equilibrium. The following table uses the same Kb value and the same standard 25°C assumption.
| Molality or Approx. Formal Concentration | Calculated [OH-] | Calculated pOH | Calculated pH |
|---|---|---|---|
| 0.10 | 7.22 × 10-3 | 2.14 | 11.86 |
| 0.50 | 1.65 × 10-2 | 1.78 | 12.22 |
| 1.00 | 2.34 × 10-2 | 1.63 | 12.37 |
| 10.0 | 7.47 × 10-2 | 1.13 | 12.87 |
| 40.0 | 1.50 × 10-1 | 0.83 | 13.18 |
The trend is clear: stronger formal loading of ethylamine pushes the solution to a higher pH, although the increase becomes progressively less dramatic because pH is logarithmic and because the base remains only partially protonated.
Common Mistakes to Avoid
- Confusing Kb with Ka. Ethylamine is a base, so use Kb unless you are working through the conjugate acid and converting constants.
- Using pH directly from concentration. Weak bases do not fully dissociate, so pH is not found by assuming [OH-] = initial base concentration.
- Ignoring the notation “m”. Lowercase m usually means molality, not molarity.
- Forgetting pOH. Because a base produces OH-, you usually calculate pOH first and then convert to pH.
- Overlooking high-concentration limitations. At 40 m, the idealized Kb model is a practical estimate, not a full activity-corrected thermodynamic treatment.
When to Use Activities Instead of Concentrations
In introductory chemistry, concentration-based equilibrium calculations are standard. In more advanced settings, however, pH is tied to activity rather than raw concentration. A very concentrated amine solution can show meaningful deviations from ideal behavior due to intermolecular interactions and changes in solvent properties. If your laboratory, industrial, or research application requires precise pH prediction, you should consult data on activity coefficients and measured solution properties rather than relying only on the simple Kb expression.
For reference-quality chemical property information, see the NIH PubChem entry for ethylamine, the NIST Chemistry WebBook entry, and university-level acid-base resources such as the University of Wisconsin weak bases tutorial. These sources are useful for checking constants, nomenclature, and general equilibrium methods.
Practical Interpretation of the Final Answer
A pH of about 13.18 means the solution is strongly basic. It is not “strongly basic” because ethylamine is a strong base in the same sense as sodium hydroxide; ethylamine remains a weak base. Instead, the pH is high because the solution is extremely concentrated. Even modest protonation of such a large amount of dissolved base generates enough hydroxide to drive the pH upward into the 13 range.
This distinction matters. Weak bases are defined by incomplete reaction with water, not by whether the resulting solution has a low or high pH. A concentrated weak base can absolutely have a very high pH, while a very dilute strong base can produce a lower pH than you might intuitively expect.
Final Takeaway
If you are asked to calculate the pH of a 40 m solution of ethylamine in a standard chemistry problem, use the weak-base equilibrium expression with the ethylamine Kb value. Solving the equilibrium gives [OH-] ≈ 0.150, pOH ≈ 0.825, and therefore pH ≈ 13.18 at 25°C. That is the conventional, correct textbook answer. The only caveat is that 40 m is highly concentrated, so the real experimental pH may differ somewhat from the idealized equilibrium estimate if non-ideal effects are included.