Calculate the pH of a 0.20 M C2H5NH2 Solution
Use this premium weak-base calculator to determine the pH, pOH, hydroxide concentration, and percent ionization of an aqueous ethylamine solution. The tool applies the equilibrium expression for a weak base and solves the chemistry accurately with a quadratic method.
Weak Base pH Calculator
Key Chemistry Setup
Reaction: C2H5NH2 + H2O ⇌ C2H5NH3+ + OH-
Base equilibrium expression: Kb = [C2H5NH3+][OH-] / [C2H5NH2]
For a 0.20 M starting solution: let x = [OH-] at equilibrium
Then: Kb = x² / (0.20 – x)
- Common textbook Kb value: 5.6 × 10-4 at 25 degrees C
- Expected behavior: Ethylamine is a weak base, so it does not fully ionize in water
- Typical answer: pH is a little above 12 for a 0.20 M solution
- Best practice: Use the quadratic solution when you want the most defensible result
Expert Guide: How to Calculate the pH of a 0.20 M C2H5NH2 Solution
To calculate the pH of a 0.20 M C2H5NH2 solution, you need to recognize first that C2H5NH2 is ethylamine, a weak Brønsted base. Weak bases do not ionize completely in water. Instead, they establish an equilibrium in which some ethylamine molecules accept protons from water to form the conjugate acid C2H5NH3+ and hydroxide ions OH-. Since pH is directly tied to the hydrogen ion concentration and indirectly tied to hydroxide ion concentration, the chemistry problem becomes an equilibrium problem rather than a simple stoichiometry problem.
The key reaction is:
C2H5NH2 + H2O ⇌ C2H5NH3+ + OH-
Because hydroxide is produced, the solution is basic. The more OH- generated, the higher the pH. However, because ethylamine is a weak base, only a fraction of the original 0.20 M actually reacts. That is why you must use the base dissociation constant, Kb, rather than assuming complete dissociation as you would for a strong base like NaOH.
Step 1: Identify the Type of Compound
Ethylamine belongs to the amine family, which behaves as a weak base in water because the nitrogen atom has a lone pair of electrons that can accept a proton. This is structurally similar to ammonia, NH3, but alkyl substitution often changes the base strength. Ethylamine is more basic than ammonia in water, so at the same concentration it produces a somewhat higher hydroxide concentration than NH3 would.
- Compound: C2H5NH2
- Name: Ethylamine
- Acid-base role: Weak base
- Conjugate acid: C2H5NH3+
- Useful constant: Kb = 5.6 × 10-4 at 25 degrees C
Step 2: Write the Equilibrium Expression
For the reaction of ethylamine with water, the base dissociation expression is:
Kb = [C2H5NH3+][OH-] / [C2H5NH2]
If the initial concentration of ethylamine is 0.20 M, and if we let x represent the amount that reacts, then the equilibrium concentrations become:
- [C2H5NH2] = 0.20 – x
- [C2H5NH3+] = x
- [OH-] = x
Substitute these into the Kb expression:
5.6 × 10-4 = x² / (0.20 – x)
This is the central equation for the problem.
Step 3: Solve for Hydroxide Concentration
There are two common ways to solve weak base problems: the approximation method and the exact quadratic method.
- Approximation method: Assume x is small compared with 0.20, so 0.20 – x is approximately 0.20. Then x² = (5.6 × 10-4)(0.20) = 1.12 × 10-4. Taking the square root gives x ≈ 0.01058 M.
- Exact method: Solve x² + (5.6 × 10-4)x – (1.12 × 10-4) = 0 with the quadratic formula. This gives x ≈ 0.01031 M.
Since x represents [OH-], the exact hydroxide concentration is about 1.03 × 10-2 M.
Step 4: Convert OH- to pOH and pH
Once hydroxide concentration is known, the rest is straightforward:
- pOH = -log[OH-]
- pH = 14.00 – pOH
Using the exact hydroxide concentration:
pOH = -log(0.01031) ≈ 1.99
pH = 14.00 – 1.99 = 12.01 to 12.02
So the pH of a 0.20 M C2H5NH2 solution is approximately 12.02.
Comparison of Exact and Approximate Solutions
In many classroom settings, instructors allow the approximation x << C when the percent ionization is low. For ethylamine at 0.20 M, the approximation is reasonable, but the exact method is still better and easy to compute with modern calculators.
| Method | [OH-] (M) | pOH | pH | Difference from Exact |
|---|---|---|---|---|
| Exact quadratic | 0.01031 | 1.99 | 12.01 to 12.02 | Baseline |
| Small-x approximation | 0.01058 | 1.98 | 12.02 | About 0.01 pH unit |
| Incorrect full dissociation assumption | 0.20 | 0.70 | 13.30 | Grossly too high |
Why You Cannot Treat Ethylamine Like a Strong Base
A common mistake is to think that because the concentration is 0.20 M, the hydroxide concentration must also be 0.20 M. That only works for strong bases that dissociate completely, such as NaOH or KOH. Ethylamine is molecular, not ionic, and it reacts only partially with water. The equilibrium constant Kb tells you how far the reaction proceeds.
If you incorrectly assumed full dissociation, you would calculate a pH near 13.30, which is far too high. The correct value near 12.02 is more than an order of magnitude lower in hydroxide concentration than the strong-base assumption predicts.
Percent Ionization of a 0.20 M Ethylamine Solution
Another useful quantity is percent ionization, which tells you what fraction of the initial base actually reacts:
Percent ionization = (x / initial concentration) × 100
Using the exact value x = 0.01031 M:
Percent ionization = (0.01031 / 0.20) × 100 ≈ 5.16%
This number explains why the approximation works moderately well but is not perfect. The reaction extent is small compared with the starting concentration, but not vanishingly small.
How Ethylamine Compares with Other Common Weak Bases
Ethylamine is stronger as a base than ammonia under standard aqueous conditions. That means for equal concentrations, ethylamine generally yields a higher [OH-] and therefore a higher pH. This comparison is useful in both general chemistry and analytical chemistry because it helps you predict the relative basicity of different nitrogen-containing compounds.
| Base | Representative Kb at 25 degrees C | pKb | Expected Basic Strength |
|---|---|---|---|
| Ammonia, NH3 | 1.8 × 10-5 | 4.74 | Weaker than ethylamine |
| Ethylamine, C2H5NH2 | 5.6 × 10-4 | 3.25 | Moderately stronger weak base |
| Methylamine, CH3NH2 | About 4.4 × 10-4 | 3.36 | Similar to ethylamine |
Detailed Walkthrough for Students
If you want a reliable procedure you can repeat on tests and homework, follow this short pattern every time you see a weak base pH question.
- Write the base-water equilibrium reaction.
- Look up or use the given Kb value.
- Set up an ICE table with initial, change, and equilibrium concentrations.
- Substitute into the Kb expression.
- Solve for x, which equals [OH-].
- Compute pOH using the negative logarithm.
- Compute pH from 14.00 – pOH.
- Check whether your answer makes sense for a weak base.
For this problem, a pH around 12 is chemically sensible. It is definitely basic, yet not as high as a fully dissociated 0.20 M strong base. That is exactly what you should expect from a weak base with a Kb in the 10-4 range.
Common Errors to Avoid
- Using Ka instead of Kb: Ethylamine is a base, so use Kb unless the problem specifically gives the conjugate-acid Ka.
- Forgetting to calculate pOH first: Weak base problems usually give OH-, not H+, directly.
- Assuming complete dissociation: This produces a pH much too high.
- Dropping the minus sign in logarithms: Remember pOH = -log[OH-].
- Rounding too early: Keep several digits until the final pH step.
How This Connects to Real Chemistry
Ethylamine and related amines matter in synthetic chemistry, pharmaceutical chemistry, industrial processing, and laboratory analysis. Understanding their pH behavior helps chemists predict protonation state, solubility, reaction conditions, buffer regions, and extraction behavior. In aqueous systems, the balance between the neutral amine and its protonated ammonium form can change dramatically with pH. That is why weak-base calculations are not just classroom exercises; they are directly tied to practical solution chemistry.
Authoritative Reference Sources
If you want deeper background on acid-base equilibria, pH, and aqueous chemistry, these authoritative resources are excellent starting points:
- LibreTexts Chemistry for broad acid-base equilibrium explanations used by many university courses.
- National Institute of Standards and Technology (NIST) for scientific standards and chemical data infrastructure.
- U.S. Environmental Protection Agency for pH fundamentals and water chemistry context.
- Brigham Young University Chemistry for university-level chemistry learning support.
Final Answer
Using Kb = 5.6 × 10-4 for ethylamine and an initial concentration of 0.20 M, the equilibrium hydroxide concentration is approximately 0.0103 M. That gives pOH ≈ 1.99 and therefore:
pH ≈ 12.02
If you need the most accurate classroom answer, report the pH as 12.01 or 12.02 depending on your rounding convention and the exact Kb value supplied by your instructor or textbook.