Calculate pH of a 4 M Solution of NH2Me
Use this premium weak-base calculator to determine the pH, pOH, hydroxide concentration, and degree of ionization for methylamine, NH2Me, also written as CH3NH2. The calculator uses the base dissociation constant Kb and solves the equilibrium exactly with the quadratic formula.
Weak Base pH Calculator
How to calculate the pH of a 4 M solution of NH2Me
Methylamine, written as NH2Me or CH3NH2, is a weak Brønsted base. That means it does not react completely with water the way a strong base such as sodium hydroxide does. Instead, only a small fraction of methylamine molecules accept a proton from water, producing methylammonium ions and hydroxide ions. The hydroxide ions are what make the solution basic and push the pH above 7. If you want to calculate the pH of a 4 M solution of NH2Me correctly, the key is to use the weak-base equilibrium expression and the base dissociation constant, Kb.
At 25 C, a widely used textbook value for the base dissociation constant of methylamine is approximately 4.4 × 10-4. Because the starting concentration here is relatively large, 4.0 M, the solution is strongly basic in appearance, but the chemistry is still governed by weak-base equilibrium. The pH is not found by assuming the full 4.0 M turns into hydroxide. Instead, we calculate the much smaller equilibrium hydroxide concentration generated by the partial reaction with water.
Step 1: Write the balanced base equilibrium
The relevant reaction is:
Here, methylamine acts as the base and accepts a proton from water. The products are the conjugate acid, methylammonium, and hydroxide. Since hydroxide is produced, the solution is basic.
Step 2: Set up an ICE table
An ICE table is the standard way to handle equilibrium concentration problems.
- Initial: [CH3NH2] = 4.0 M, [CH3NH3+] = 0, [OH–] = 0
- Change: -x, +x, +x
- Equilibrium: [CH3NH2] = 4.0 – x, [CH3NH3+] = x, [OH–] = x
This lets us convert the chemistry into a solvable algebraic expression.
Step 3: Use the Kb expression
For methylamine, the base dissociation expression is:
Substitute the ICE table values:
Because x is not astronomically small compared with the concentration scale used in pH problems, the most rigorous way is to solve this exactly. Multiply both sides:
Now apply the quadratic formula:
With a = 1, b = 0.00044, and c = -0.00176, the physically meaningful root is:
That means the equilibrium hydroxide concentration is about 0.0417 M.
Step 4: Convert [OH-] into pOH and pH
Use the standard relationship:
Substituting x:
Then at 25 C:
So the pH of a 4 M solution of NH2Me is approximately 12.62.
Why methylamine is basic
Methylamine contains a nitrogen atom with a lone pair of electrons. That lone pair is able to accept a proton, which is the defining behavior of a Brønsted base. Compared with ammonia, methylamine is actually a somewhat stronger weak base because the methyl group donates electron density toward nitrogen, making proton acceptance more favorable. This is why the Kb for methylamine is larger than the Kb for ammonia under standard conditions.
Even so, methylamine is still not a strong base. The overwhelming majority of CH3NH2 molecules remain unprotonated in solution. In the 4.0 M example, the calculated hydroxide concentration is only around 0.0417 M, and the percent ionization is roughly 1.04%. This is a classic hallmark of a weak base: high initial concentration, basic pH, but only modest dissociation at equilibrium.
Shortcut approximation versus exact solution
Many chemistry courses teach the weak-base shortcut:
For methylamine at 4.0 M:
This gives a pH of approximately 12.623, which is extremely close to the exact quadratic result. The approximation works well here because x is still small relative to the initial 4.0 M concentration. Specifically, x/C is just over 1%, which comfortably satisfies the usual 5% guideline for neglecting x in the denominator.
That said, the exact quadratic method is always the safest choice, especially in calculators, because it avoids approximation error entirely. On pages like this one, using the exact method also gives students a more dependable answer when they test unusual Kb values or concentrations.
| Method | Calculated [OH-] (M) | pOH | pH at 25 C | Percent ionization |
|---|---|---|---|---|
| Exact quadratic solution | 0.04169 | 1.380 | 12.620 | 1.042% |
| Weak-base approximation | 0.04195 | 1.377 | 12.623 | 1.049% |
| Difference | 0.00026 | 0.003 | 0.003 | 0.007 percentage points |
Worked interpretation of the result
A pH of about 12.62 tells you the solution is strongly basic from a practical point of view. However, that does not mean methylamine is a strong base in the thermodynamic sense. The distinction matters. A strong base dissociates essentially completely, while a weak base like methylamine establishes an equilibrium. In this case, even though the pH is high, the equilibrium still strongly favors the undissociated CH3NH2. This is why Kb and equilibrium calculations remain central.
If you are doing this problem for general chemistry, analytical chemistry, or equilibrium review, the instructor usually expects several pieces of reasoning:
- Recognize NH2Me as methylamine, a weak base.
- Write the base hydrolysis equilibrium with water.
- Use an ICE table.
- Insert concentrations into the Kb expression.
- Solve for x and identify x as [OH–].
- Convert [OH–] to pOH and then to pH.
If you show those steps clearly, your work will usually earn full credit even if your rounding differs slightly from a textbook answer key.
How concentration affects the pH of methylamine solutions
As the initial concentration of methylamine rises, the hydroxide concentration at equilibrium also rises, and the pH increases. But the increase is not linear. Because the equilibrium relation involves a square root in the common approximation, doubling the concentration does not double the hydroxide concentration or the pH shift. This is why high-concentration weak-base solutions often produce surprisingly moderate pH changes compared with strong bases.
| Initial CH3NH2 concentration (M) | Using Kb = 4.4 × 10^-4 | Exact [OH-] (M) | Calculated pH | Percent ionization |
|---|---|---|---|---|
| 0.10 | Weak base equilibrium | 0.00642 | 11.81 | 6.42% |
| 0.50 | Weak base equilibrium | 0.01462 | 12.16 | 2.92% |
| 1.00 | Weak base equilibrium | 0.02076 | 12.32 | 2.08% |
| 4.00 | Weak base equilibrium | 0.04169 | 12.62 | 1.04% |
| 5.00 | Weak base equilibrium | 0.04670 | 12.67 | 0.93% |
Notice the pattern in the table above. As concentration increases, pH rises, but percent ionization falls. This is a very common equilibrium trend for weak acids and weak bases. A larger starting concentration suppresses the fraction that ionizes, even though the absolute amount of hydroxide produced still increases.
Common mistakes students make
- Treating NH2Me as a strong base. If you assume all 4.0 M becomes OH–, you get a completely unrealistic pH for a weak base problem.
- Using Ka instead of Kb. Methylamine is a base, so Kb is the natural equilibrium constant unless the problem is framed through its conjugate acid.
- Forgetting that x equals [OH-]. In the ICE table for this reaction, the hydroxide concentration created is x.
- Mixing up pH and pOH. For bases, you usually calculate pOH first, then convert to pH.
- Using too few significant figures. Since logarithms compress values, rounding too early can shift the final pH by a few hundredths.
Relationship to pKa and the conjugate acid
You may also see methylamine discussed through its conjugate acid, CH3NH3+. At 25 C, the water ion-product relationship is:
If Kb = 4.4 × 10-4, then:
The corresponding pKa is about 10.64. That value is useful when working with methylamine buffers or titration problems involving CH3NH2 and CH3NH3+. For the direct pH of a pure methylamine solution, though, the Kb route is simpler and more direct.
Authoritative references for acid-base chemistry
If you want to verify constants or review acid-base fundamentals from authoritative educational sources, these references are helpful:
- NIST Chemistry WebBook (.gov) entry for methylamine
- U.S. Environmental Protection Agency (.gov) overview of pH concepts
- MIT OpenCourseWare (.edu) chemistry materials on equilibrium and acid-base principles
Final answer
Using a typical value of Kb = 4.4 × 10-4 for methylamine at 25 C, the pH of a 4.0 M NH2Me solution is:
pH ≈ 12.62
The exact equilibrium calculation gives:
- [OH–] ≈ 0.04169 M
- pOH ≈ 1.380
- pH ≈ 12.620
- Percent ionization ≈ 1.042%