Calculate the pH of a 0.73 M Methylamine Solution
Use this interactive weak-base calculator to determine the pH, pOH, hydroxide concentration, percent ionization, and equilibrium composition for methylamine in water. The default values are set for a 0.73 M methylamine solution at 25 degrees Celsius using a common literature Kb value for CH3NH2.
Weak Base pH Calculator
Quick Chemistry Snapshot
- Methylamine is a weak base with formula CH3NH2.
- In water it reacts as: CH3NH2 + H2O ⇌ CH3NH3+ + OH-.
- For a weak base, pOH is found first from equilibrium [OH-].
- Then convert using pH = 14.00 – pOH at 25 degrees Celsius.
The chart compares the initial methylamine concentration with the equilibrium amounts of CH3NH2, CH3NH3+, and OH-.
How to calculate the pH of a 0.73 M methylamine solution
To calculate the pH of a 0.73 M methylamine solution, you treat methylamine as a weak Brønsted base. It does not fully dissociate in water the way a strong base like sodium hydroxide does. Instead, only a fraction of the dissolved methylamine molecules accept protons from water, producing methylammonium ions and hydroxide ions. The amount of hydroxide formed is controlled by the base dissociation constant, Kb.
Methylamine has the formula CH3NH2. In water, the equilibrium reaction is:
The most common textbook value of the base dissociation constant for methylamine at 25 degrees Celsius is approximately 4.4 x 10^-4. Because the initial concentration in this problem is relatively high at 0.73 M, the resulting solution is definitely basic, but not as basic as a 0.73 M strong base would be. That distinction is exactly why weak base equilibrium math matters.
Step 1: Write the Kb expression
For the reaction above, the equilibrium constant expression is:
If the initial methylamine concentration is 0.73 M and no methylammonium or hydroxide is added at the start, then an ICE table can be built:
- Initial: [CH3NH2] = 0.73, [CH3NH3+] = 0, [OH-] = 0
- Change: [CH3NH2] decreases by x, [CH3NH3+] increases by x, [OH-] increases by x
- Equilibrium: [CH3NH2] = 0.73 – x, [CH3NH3+] = x, [OH-] = x
Substitute those terms into the Kb expression:
Step 2: Solve for hydroxide concentration
You can solve this expression two ways. The first is the common weak-base approximation, where x is assumed to be small compared with 0.73. In that case:
Then:
That means the hydroxide ion concentration is about 0.0179 M. Since x is only a few percent of 0.73, the approximation works reasonably well.
For a more exact result, solve the quadratic equation from:
The physically meaningful root gives x very close to 0.0177 M. The exact and approximate answers are very similar, which confirms the chemistry is behaving as expected.
Step 3: Convert [OH-] into pOH and pH
Once you know the hydroxide concentration, calculate pOH:
Using the exact value x ≈ 0.0177 M:
At 25 degrees Celsius, use:
So:
Why methylamine does not give the same pH as a strong base
Many students initially think that any base with a concentration as high as 0.73 M must produce an extremely high pH. The key point is that concentration alone is not enough. Base strength matters. A strong base such as NaOH essentially dissociates completely, so a 0.73 M NaOH solution would have [OH-] close to 0.73 M. Methylamine is a weak base, so only a small fraction converts into hydroxide.
This difference is dramatic. For 0.73 M NaOH, the pOH would be about 0.14 and the pH would be about 13.86. For 0.73 M methylamine, the pOH is near 1.75 and the pH is near 12.25. Both are basic, but the strong base is more than an order of magnitude richer in hydroxide ions.
| Solution | Initial Base Concentration | Assumed [OH-] | pOH | pH at 25 degrees Celsius |
|---|---|---|---|---|
| 0.73 M methylamine | 0.73 M | 0.0177 M | 1.75 | 12.25 |
| 0.73 M NaOH | 0.73 M | 0.73 M | 0.14 | 13.86 |
| 0.73 M ammonia | 0.73 M | 0.0170 M using Kb = 1.8 x 10^-5? No, much lower, about 0.0036 M | 2.44 | 11.56 |
The ammonia row is especially helpful for comparison. Ammonia is also a weak base, but it is weaker than methylamine. Methylamine is more basic because the methyl group donates electron density to the nitrogen atom, increasing its ability to accept a proton. This is why methylamine generally has a larger Kb than ammonia and therefore produces a higher pH at the same formal concentration.
Exact versus approximate solution
In introductory chemistry, you are often encouraged to check whether the small-x approximation is valid. For weak acids and weak bases, the approximation works best when the degree of ionization is relatively low. The rule of thumb is that if x is less than 5 percent of the initial concentration, the approximation is usually acceptable for many classroom problems.
For methylamine at 0.73 M:
- Approximate x is about 0.0179 M
- Percent ionization is roughly (0.0179 / 0.73) x 100 ≈ 2.45%
Because 2.45 percent is under 5 percent, the approximation is acceptable. Still, the quadratic solution is cleaner for a calculator because it avoids avoidable error and always works when the approximation begins to break down.
| Method | Equation Used | Calculated [OH-] | Calculated pH | When to Use |
|---|---|---|---|---|
| Weak-base approximation | x ≈ √(KbC) | 0.0179 M | 12.25 | Fast classroom estimate when ionization is small |
| Exact quadratic solution | x = (-Kb + √(Kb² + 4KbC)) / 2 | 0.0177 M | 12.25 | Best for calculators, exams, and rigorous work |
Common mistakes when calculating the pH of methylamine
1. Using pH directly from base concentration
A frequent mistake is to assume [OH-] equals 0.73 M. That would only be true for a strong base that dissociates completely. Methylamine is a weak base, so the concentration of hydroxide produced is much smaller than the formal concentration of methylamine added.
2. Confusing Kb with Ka
Methylamine is a base, so Kb should be used. If you are given the Ka of its conjugate acid, methylammonium, then you can convert using the relationship Kw = Ka x Kb at 25 degrees Celsius, where Kw = 1.0 x 10^-14.
3. Forgetting to calculate pOH first
Because hydroxide is produced in the base equilibrium, the natural quantity you calculate is [OH-], then pOH, then pH. Skipping the pOH step often leads to sign or log mistakes.
4. Ignoring temperature assumptions
The common pH relation pH + pOH = 14.00 is strictly tied to 25 degrees Celsius unless your instructor specifies otherwise. In many classroom and online calculator contexts, that is the accepted standard assumption.
Detailed worked example for 0.73 M CH3NH2
- Write the equilibrium reaction: CH3NH2 + H2O ⇌ CH3NH3+ + OH-
- Set the initial concentration of methylamine to 0.73 M.
- Let x equal the amount of methylamine that reacts.
- At equilibrium, [OH-] = x and [CH3NH2] = 0.73 – x.
- Use Kb = 4.4 x 10^-4 and solve x^2 / (0.73 – x) = 4.4 x 10^-4.
- Obtain x ≈ 0.0177 M.
- Compute pOH = -log(0.0177) ≈ 1.75.
- Compute pH = 14.00 – 1.75 ≈ 12.25.
If your instructor expects a limited-significant-figure answer, you would usually report the final pH as 12.25 or 12.3 depending on the format and the precision of the supplied Kb value.
How concentration affects the pH of methylamine
As the initial concentration of methylamine increases, the pH increases, but not in a perfectly linear way. Since weak-base equilibria follow a square-root style dependence under the usual approximation, doubling concentration does not double [OH-] and does not create a one-to-one pH shift. This is why charts are useful for visualizing weak electrolyte behavior.
For example, using Kb = 4.4 x 10^-4 at 25 degrees Celsius:
- 0.010 M methylamine gives a pH near 11.32
- 0.100 M methylamine gives a pH near 11.81
- 0.730 M methylamine gives a pH near 12.25
- 1.000 M methylamine gives a pH near 12.32
This pattern reflects the logarithmic nature of pH and the equilibrium-limited formation of OH-. It also explains why a large increase in concentration causes only a moderate increase in pH.
Authoritative chemistry references
If you want to verify equilibrium concepts, pH definitions, or weak base calculations using trusted sources, these references are strong starting points:
- Chemistry educational resources hosted by university partners
- U.S. Environmental Protection Agency chemistry and water quality resources
- NIST Chemistry WebBook
- MIT Chemistry educational content
For direct authority-domain examples relevant to acid-base chemistry and physical chemistry data, government and university references such as the NIST Chemistry WebBook, educational materials from MIT Chemistry, and water chemistry guidance from the U.S. EPA are especially useful.
Bottom line
To calculate the pH of a 0.73 M methylamine solution, you use weak-base equilibrium rather than full dissociation. Start with the methylamine Kb value, build an ICE table, solve for the hydroxide concentration, then convert to pOH and finally pH. Using Kb = 4.4 x 10^-4 at 25 degrees Celsius gives an exact pH of about 12.25. That result is chemically sensible because methylamine is clearly basic, but it remains much less dissociated than a strong base of the same formal concentration.
If you want a fast practical answer, remember this benchmark: 0.73 M methylamine has a pH of approximately 12.25 at 25 degrees Celsius.