Calculate The Ph Of A 0.26M Methylamine Solution

Use this interactive weak-base calculator to find pOH, pH, hydroxide concentration, percent ionization, and the exact equilibrium result for aqueous methylamine, CH₃NH₂.

Default concentration

0.26 M

Typical K_b

4.4 × 10^-4

Expected pH range

~12.03

Base strength class

Weak base

Methylamine reacts with water according to: CH₃NH₂ + H₂O ⇌ CH₃NH₃⁺ + OH^–. Because K_b is much smaller than 1, only a small fraction ionizes, but the solution is still strongly basic enough to give a pH a little above 12 at 0.26 M.

How to calculate the pH of a 0.26 M methylamine solution

To calculate the pH of a 0.26 M methylamine solution, you treat methylamine, CH₃NH₂, as a weak base in water. Unlike a strong base such as sodium hydroxide, methylamine does not dissociate completely. Instead, it establishes an equilibrium with water, producing methylammonium ions and hydroxide ions. The hydroxide concentration produced at equilibrium determines the pOH, and from pOH you can find the pH. For a standard general chemistry calculation at 25°C, a commonly used value for the base dissociation constant of methylamine is K_b = 4.4 × 10^-4.

CH3NH2 + H2O ⇌ CH3NH3+ + OH-

The equilibrium expression is:

Kb = ([CH3NH3+][OH-]) / [CH3NH2]

Start with an initial concentration of 0.26 M methylamine and assume no product is present initially. If x is the amount that reacts, then at equilibrium the concentrations become 0.26 – x for CH₃NH₂, x for CH₃NH₃⁺, and x for OH^–. This gives:

4.4 × 10^-4 = x^2 / (0.26 – x)

You can solve that equation exactly using the quadratic formula, or approximately using the weak-base shortcut x ≈ √(K_bC). Both methods give nearly the same answer here because methylamine ionizes only by a few percent under these conditions.

Exact calculation

Using the quadratic setup:

x^2 + Kb x – Kb C = 0

with C = 0.26 and K_b = 4.4 × 10^-4, the positive root gives:

[OH-] = x = (-Kb + √(Kb^2 + 4KbC)) / 2

Substituting values gives [OH^–] ≈ 0.01049 M. Then:

pOH = -log(0.01049) ≈ 1.98

pH = 14.00 – 1.98 ≈ 12.02

So the pH of a 0.26 M methylamine solution is approximately 12.02 at 25°C when using K_b = 4.4 × 10^-4.

Approximation method

The approximation is often taught first because it is fast and usually accurate for weak acids and weak bases when ionization is small relative to the starting concentration. Here, you use:

x ≈ √(KbC) = √((4.4 × 10^-4)(0.26)) ≈ 0.0107 M

Then:

pOH ≈ -log(0.0107) ≈ 1.97

pH ≈ 14.00 – 1.97 ≈ 12.03

The approximation differs from the exact value by only about 0.01 pH units, which is more than acceptable for many classroom and exam situations. This is why many instructors allow or even expect the square-root method first, followed by a quick percent-ionization check.

Step by step method for students

1. Write the weak-base reaction: CH₃NH₂ + H₂O ⇌ CH₃NH₃⁺ + OH^–.
2. Identify the given concentration, C = 0.26 M.
3. Use a trusted K_b value for methylamine, commonly 4.4 × 10^-4 at 25°C.
4. Set up an ICE table with initial, change, and equilibrium concentrations.
5. Solve for x, which equals [OH^–] at equilibrium.
6. Compute pOH = -log[OH^–].
7. Use pH = 14.00 – pOH at 25°C.
8. Check percent ionization to verify whether the approximation was valid.

ICE table for methylamine

An ICE table makes the chemistry transparent and reduces sign mistakes. For this problem:

Species	Initial (M)	Change (M)	Equilibrium (M)
CH3NH2	0.26	-x	0.26 – x
CH3NH3^+	0	+x	x
OH^–	0	+x	x

That table leads directly to the equilibrium expression. One reason students like this setup is that it works for weak acids, weak bases, hydrolysis of salts, and many buffer problems with only minor adjustments. If you can build the ICE table correctly, the rest of the algebra is usually straightforward.

Comparison of exact and approximate results

Because methylamine is a weak base but not an extremely weak one, exact and approximate methods are very close at 0.26 M. The table below shows how the two methods compare using K_b = 4.4 × 10^-4 and pK_w = 14.00.

Method	[OH^–] (M)	pOH	pH	Percent ionization
Exact quadratic	0.01049	1.979	12.021	4.03%
Weak-base approximation	0.01070	1.971	12.029	4.11%
Difference	0.00021	0.008	0.008	0.08 percentage points

Notice that percent ionization is only about 4%. That is small enough that replacing 0.26 – x with 0.26 is a good approximation, although strictly speaking many instructors use a 5% guideline. Since the ionization is below 5%, the shortcut is justified here.

How concentration changes the pH

The concentration of methylamine strongly influences pH because more dissolved base provides more molecules that can react with water and create hydroxide ions. However, the increase is not linear. Since weak-base ionization often follows an x ≈ √(K_bC) trend, pH rises more gradually than concentration itself.

Methylamine concentration (M)	Approximate [OH^–] (M)	Approximate pH at 25°C	Approximate percent ionization
0.010	0.00210	11.32	21.0%
0.050	0.00469	11.67	9.38%
0.100	0.00663	11.82	6.63%
0.260	0.01070	12.03	4.11%
0.500	0.01483	12.17	2.97%

This trend shows another important concept: as concentration increases, percent ionization often decreases for weak electrolytes. That might feel counterintuitive at first, but it follows directly from equilibrium behavior. A more concentrated weak base produces more OH^– in absolute terms, yet a smaller fraction of the total molecules ionize.

Common mistakes when solving this problem

• Using K_a instead of K_b. Methylamine is a base, so use K_b unless you are given the conjugate acid data and explicitly converting.
• Forgetting that the equilibrium produces OH^–, not H⁺. You must calculate pOH first unless you directly convert.
• Assuming complete dissociation. Methylamine is not a strong base.
• Using pH = -log[OH^–]. That formula gives pOH, not pH.
• Ignoring temperature. If the problem is not at 25°C, pK_w is not exactly 14.00.
• Rounding too early. Keep extra digits until the final step to avoid drift in pH.

Why the answer is around 12 and not 13 or 14

A 0.26 M solution sounds concentrated, so it is tempting to think the pH should be extremely high. But pH depends on the hydroxide concentration actually present at equilibrium, not on the nominal base concentration alone. For methylamine, only a small portion of the dissolved molecules react with water. The equilibrium [OH^–] is about 0.0105 M, which corresponds to a pOH near 1.98 and a pH near 12.02. That is basic, but still much lower than the pH of a 0.26 M strong base such as NaOH, which would have [OH^–] ≈ 0.26 M and a pH well above 13.

Methylamine versus a strong base

This comparison is useful for intuition. If the same 0.26 M concentration belonged to sodium hydroxide, a strong base, the hydroxide concentration would essentially equal 0.26 M because dissociation is nearly complete. Then pOH would be about 0.585 and pH would be about 13.42. By contrast, 0.26 M methylamine gives [OH^–] around 0.0105 M and pH around 12.02. That difference of roughly 1.4 pH units corresponds to a dramatic change in hydroxide concentration and reflects the weak-base nature of methylamine.

Quick answer

For a 0.26 M methylamine solution using K_b = 4.4 × 10^-4 at 25°C, the pH is approximately 12.02 by the exact method and 12.03 by the common square-root approximation.

When to use the exact quadratic formula

Use the exact method whenever high precision matters, when percent ionization is not very small, or when your instructor specifically requires it. The approximation x ≈ √(K_bC) is fast, but it assumes x is negligible compared with the initial concentration. At lower concentrations or with relatively larger equilibrium constants, that assumption can fail. In those cases the denominator 0.26 – x cannot be simplified safely, and the quadratic should be solved directly.

Authoritative chemistry references

For deeper study of acid-base equilibria and water chemistry, consult these reliable sources:

• Chemistry LibreTexts for broad educational coverage of weak acid and weak base equilibria.
• U.S. Environmental Protection Agency (.gov) for pH fundamentals and water chemistry context.
• Princeton University Chemistry (.edu) for university-level chemistry resources and instructional material.

Final conclusion

If you are asked to calculate the pH of a 0.26 M methylamine solution, the chemistry is a classic weak-base equilibrium problem. Write the reaction with water, use K_b for methylamine, solve for the hydroxide ion concentration, and then convert pOH to pH. At 25°C with K_b = 4.4 × 10^-4, the exact pH is about 12.02. The approximation method gives about 12.03, which confirms the result quickly and shows that only a small fraction of methylamine is protonated in water. If you remember one takeaway, make it this: methylamine is a weak base, so you must use equilibrium, not complete dissociation, to get the correct pH.