Calculate the pH of a 0.100 M Methylamine CH3NH2 Solution
Use this interactive weak base calculator to find pH, pOH, hydroxide concentration, conjugate acid concentration, and percent ionization for aqueous methylamine. The tool uses the weak base equilibrium relationship with an exact quadratic solution for high accuracy.
Weak Base pH Calculator
How to Calculate the pH of a 0.100 M Methylamine CH3NH2 Solution
Methylamine, written as CH3NH2, is a classic example of a weak Brønsted-Lowry base in water. When dissolved, it does not react completely like a strong base such as sodium hydroxide. Instead, only a fraction of methylamine molecules accept a proton from water to form the conjugate acid CH3NH3+ and hydroxide ions OH−. Because pH depends on the hydroxide concentration generated at equilibrium, calculating the pH of a 0.100 M methylamine solution requires an equilibrium approach rather than a simple direct dissociation formula.
The key equilibrium is:
CH3NH2 + H2O ⇌ CH3NH3+ + OH−
For this reaction, the base dissociation constant is:
Kb = [CH3NH3+][OH−] / [CH3NH2]
At 25 C, methylamine is commonly listed with a Kb of about 4.4 × 10-4. That number tells you methylamine is clearly basic, but still weak enough that equilibrium mathematics matter. If you are asked to calculate the pH of a 0.100 M methylamine solution in a chemistry class, lab report, exam, or homework problem, the standard path is to write the ICE table, solve for x, compute pOH from hydroxide concentration, and finally convert to pH.
Step 1: Set up the ICE table
Let the initial methylamine concentration be 0.100 M and let x represent the amount that reacts with water.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| CH3NH2 | 0.100 | -x | 0.100 – x |
| CH3NH3+ | 0 | +x | x |
| OH− | 0 | +x | x |
Substitute those equilibrium terms into the Kb expression:
4.4 × 10-4 = x² / (0.100 – x)
Step 2: Solve for x
Many textbook problems use the weak base approximation and assume x is small compared with 0.100. If you do that, the denominator becomes approximately 0.100, giving:
x² / 0.100 = 4.4 × 10-4
x² = 4.4 × 10-5
x = 6.63 × 10-3 M
This x value is the equilibrium hydroxide concentration, so:
[OH−] ≈ 0.00663 M
Because x is about 6.6 percent of the starting concentration, the approximation is acceptable for many classroom purposes, but it is not perfectly tiny. An exact quadratic solution is more rigorous and is what this calculator uses by default.
Using the exact quadratic:
x² + Kb x – Kb C = 0
where C = 0.100 M and Kb = 4.4 × 10-4.
The physically meaningful root gives:
x ≈ 0.00642 M
So the more exact hydroxide concentration is:
[OH−] ≈ 6.42 × 10-3 M
Step 3: Convert hydroxide concentration to pOH
The formula is:
pOH = -log[OH−]
Using the exact result:
pOH = -log(0.00642) ≈ 2.193
Step 4: Convert pOH to pH
At 25 C:
pH + pOH = 14.00
Therefore:
pH = 14.00 – 2.193 = 11.807
So the pH of a 0.100 M methylamine solution is approximately 11.81 when calculated with the exact method and a Kb of 4.4 × 10-4.
Final answer
For a 0.100 M CH3NH2 solution, pH ≈ 11.81 at 25 C.
Why methylamine is basic but not strongly basic
Methylamine contains a nitrogen atom with a lone pair that can accept a proton from water. That proton-accepting behavior makes it a base. However, not every methylamine molecule reacts, because the equilibrium lies only partially to the right. This is why methylamine is called a weak base. In practical terms, weak bases require equilibrium calculations because only some of the dissolved base generates OH−.
Organic amines such as methylamine are generally more basic than ammonia because the methyl group donates electron density toward nitrogen. This electron donation slightly increases the tendency of the nitrogen lone pair to accept a proton. As a result, methylamine has a larger Kb than ammonia and will produce a somewhat higher pH at the same concentration.
Exact method versus approximation
Students are often taught a shortcut for weak acid and weak base problems: if x is small compared with the initial concentration, replace 0.100 – x with 0.100. This can save time, and it is often close enough. Still, if precision matters, the exact quadratic solution is better. For 0.100 M methylamine, the difference is modest but real.
| Method | [OH−] (M) | pOH | pH | Difference from exact pH |
|---|---|---|---|---|
| Exact quadratic | 0.00642 | 2.193 | 11.807 | 0.000 |
| Approximation | 0.00663 | 2.179 | 11.821 | +0.014 |
The pH difference here is only around 0.01 to 0.02 pH units, which is usually acceptable in introductory work. But in advanced analytical chemistry, thermodynamics, or calibrated pH modeling, using the exact method is preferable.
Species present at equilibrium
Once the system reaches equilibrium, the solution contains mostly unreacted methylamine, a smaller amount of methylammonium ion CH3NH3+, and hydroxide ion OH−. Because the reaction stoichiometry is one-to-one, the concentrations of CH3NH3+ and OH− formed by the base are equal, ignoring the tiny background contribution from water autoionization.
- Initial CH3NH2: 0.100 M
- Equilibrium CH3NH2: about 0.0936 M
- Equilibrium CH3NH3+: about 0.00642 M
- Equilibrium OH−: about 0.00642 M
- Percent ionization: about 6.42%
This percent ionization helps you see why weak base behavior matters. Most molecules remain as CH3NH2, but enough react to make the solution strongly basic on the pH scale.
Comparison with other common weak bases
To put methylamine in context, it helps to compare it with ammonia and some related weak bases. The values below are representative 25 C textbook constants. Exact values can vary slightly by source and ionic strength, but these are widely used instructional numbers.
| Weak base | Formula | Typical Kb at 25 C | Approximate pH at 0.100 M |
|---|---|---|---|
| Methylamine | CH3NH2 | 4.4 × 10-4 | 11.81 |
| Ammonia | NH3 | 1.8 × 10-5 | 11.13 |
| Pyridine | C5H5N | 1.7 × 10-9 | 8.12 |
This comparison shows why methylamine gives a notably higher pH than ammonia at the same molarity. A larger Kb means more extensive protonation of the base and greater hydroxide production.
Common mistakes when solving this problem
- Using Ka instead of Kb. Methylamine is a base, so use Kb unless the problem gives pKa of the conjugate acid and asks you to convert.
- Forgetting the ICE table. Weak base problems become much easier and more reliable when concentrations are organized systematically.
- Confusing pOH and pH. The equilibrium gives [OH−], so compute pOH first, then convert to pH.
- Applying the 14.00 relationship at the wrong temperature. The equation pH + pOH = 14.00 is exact only at 25 C in basic classroom treatment.
- Assuming complete dissociation. If you treated 0.100 M methylamine as a strong base, you would predict pOH = 1 and pH = 13, which is far too high.
Shortcut using pKb
Some instructors prefer a pKb route. Since pKb = -log(Kb), for methylamine:
pKb = -log(4.4 × 10-4) ≈ 3.36
For a weak base of concentration C, an approximation often used is:
pOH ≈ 1/2 (pKb – log C)
With C = 0.100 M, log(0.100) = -1, so:
pOH ≈ 1/2 (3.36 – (-1)) = 1/2 (4.36) = 2.18
Then:
pH ≈ 14.00 – 2.18 = 11.82
This shortcut matches the approximation method and again lands very close to the exact answer.
When real solutions may differ from the simple model
Real laboratory solutions do not always behave exactly like ideal classroom solutions. Measured pH can shift slightly because of temperature variation, ionic strength effects, dissolved carbon dioxide, meter calibration, and concentration uncertainty. In more advanced chemistry, activities can replace concentrations, and equilibrium constants may be adjusted for conditions that deviate from infinite dilution. Still, for general chemistry and most practical calculations, using 0.100 M, Kb = 4.4 × 10-4, and 25 C provides an excellent answer.
Authoritative references and further reading
If you want to verify definitions, acid-base theory, or pH fundamentals, these educational and government resources are excellent places to start:
- LibreTexts Chemistry educational resource
- U.S. Environmental Protection Agency pH overview
- University of Wisconsin Chemistry resources
Summary
To calculate the pH of a 0.100 M methylamine solution, start with the equilibrium reaction of methylamine with water, write the Kb expression, construct an ICE table, solve for hydroxide concentration, and convert that result into pOH and then pH. Using the exact quadratic with Kb = 4.4 × 10-4 gives [OH−] ≈ 0.00642 M, pOH ≈ 2.193, and pH ≈ 11.807. Rounded suitably, the solution has a pH of 11.81.