Calculate The Ph Of A 0.25 M Solution Of Ethylamine

Use this premium calculator to estimate the pH, pOH, hydroxide concentration, percent ionization, and equilibrium concentrations for aqueous ethylamine. It supports either direct molarity input or a molality to molarity conversion using solution density.

Expert guide: how to calculate the pH of a 0.25 m solution of ethylamine

Ethylamine is a weak base with the formula C₂H₅NH₂. When dissolved in water, it accepts a proton from water to produce its conjugate acid, ethylammonium, and hydroxide ion. Because hydroxide is formed, the solution becomes basic and its pH rises above 7. If your goal is to calculate the pH of a 0.25 m solution of ethylamine, the key idea is that weak bases do not dissociate completely. Instead, they establish an equilibrium, and the pH must be found from that equilibrium.

The reaction is:

C2H5NH2 + H2O ⇌ C2H5NH3+ + OH-

The base dissociation constant for ethylamine at 25 C is commonly taken to be around K_b = 5.6 × 10^-4, although small source to source variation exists. That value places ethylamine among the stronger common weak bases, stronger than ammonia and weaker than some more strongly electron donating substituted amines. In practice, this means a 0.25 m or approximately 0.25 M solution has a pH that is clearly basic, typically a little above 11.

Step 1: decide whether 0.25 m is treated as molality or molarity

In chemistry notation, a lowercase m usually means molality, which is moles of solute per kilogram of solvent. An uppercase M means molarity, which is moles of solute per liter of solution. Introductory pH problems are sometimes written loosely, and many textbook examples proceed as though a dilute aqueous solution can be treated as if molality and molarity are nearly the same. For a 0.25 m aqueous ethylamine solution, that approximation is usually acceptable because the concentration is modest and the density is close to 1.00 g/mL.

If you want a more careful conversion from molality to molarity, use:

M = (1000 × d × m) / (1000 + m × MW)

where d is the solution density in g/mL, m is molality, and MW is the molar mass of ethylamine, 45.08 g/mol. If d = 1.00 g/mL and m = 0.25, then:

M ≈ (1000 × 1.00 × 0.25) / (1000 + 0.25 × 45.08) ≈ 0.247 M

This is extremely close to 0.25 M, which is why many classroom calculations proceed directly with 0.25 as the effective concentration.

Step 2: write the Kb expression

For the equilibrium C₂H₅NH₂ + H₂O ⇌ C₂H₅NH₃⁺ + OH^–, the equilibrium expression is:

Kb = [C2H5NH3+][OH-] / [C2H5NH2]

Water is omitted because it is the solvent. If the initial effective concentration of ethylamine is C and the amount that reacts is x, then at equilibrium:

• [C₂H₅NH₂] = C – x
• [C₂H₅NH₃⁺] = x
• [OH^–] = x

Substituting these into the K_b expression gives:

Kb = x² / (C – x)

Step 3: solve for hydroxide concentration

If you use the exact method, you solve the quadratic form:

x² + Kb x – Kb C = 0

which gives:

x = (-Kb + √(Kb² + 4KbC)) / 2

Using K_b = 5.6 × 10^-4 and C = 0.247 M:

x ≈ (-0.00056 + √((0.00056)² + 4(0.00056)(0.247))) / 2 ≈ 0.0115 M

Therefore, [OH^–] ≈ 0.0115 M. If you instead use the common weak base approximation x much less than C, then:

x ≈ √(KbC) = √(5.6 × 10^-4 × 0.247) ≈ 0.0118 M

That approximation is very close. The reason is that the degree of ionization is only a few percent, so the drop from C to C – x is not large compared with the initial concentration.

Step 4: convert hydroxide concentration to pOH and pH

Once [OH^–] is known, calculate pOH:

pOH = -log[OH-]

With [OH^–] ≈ 0.0115 M:

pOH ≈ 1.94

At 25 C, use pH + pOH = 14.00:

pH = 14.00 – 1.94 ≈ 12.06

So the pH of a 0.25 m solution of ethylamine is approximately 12.06, depending on the exact K_b value and whether you treat 0.25 m as strictly molal or approximately molar.

Why ethylamine is more basic than ammonia

A useful conceptual check is to compare ethylamine with ammonia. The ethyl group attached to nitrogen donates electron density through the inductive effect. This makes the nitrogen lone pair more available to accept a proton, increasing basicity in water compared with NH₃. That is why ethylamine has a larger K_b and a smaller pK_b than ammonia. A stronger weak base produces more hydroxide at the same formal concentration, resulting in a higher pH.

Base	Approximate Kb at 25 C	Approximate pKb	Basicity comment
Ammonia, NH3	1.8 × 10^-5	4.74	Common reference weak base in general chemistry
Methylamine, CH3NH2	4.4 × 10^-4	3.36	More basic than ammonia because of alkyl electron donation
Ethylamine, C2H5NH2	5.6 × 10^-4	3.25	Slightly more basic than methylamine in many tabulations
Dimethylamine, (CH3)2NH	5.4 × 10^-4	3.27	Strong weak base, often close to ethylamine in water
Aniline, C6H5NH2	4.3 × 10^-10	9.37	Much weaker because the lone pair is delocalized into the ring

ICE table method for a clean exam style solution

If you are solving this by hand for class, using an ICE table is the clearest approach:

1. Write the equilibrium reaction.
2. Set the initial concentration of ethylamine to 0.247 M or 0.250 M depending on your assumption.
3. Let the change be -x for ethylamine and +x for both products.
4. Write the equilibrium row as C – x, x, and x.
5. Insert into K_b and solve for x.
6. Convert x to pOH, then to pH.

Many students lose points not because the chemistry is difficult, but because they skip the equilibrium setup or forget that weak bases require pOH first. Remember this pattern: weak base gives OH^–, so solve for [OH^–], then compute pOH, then pH.

How accurate is the x much less than C approximation here?

The approximation is valid when the amount dissociated is small relative to the initial concentration. In many courses, a 5 percent rule is used as a quick check. For ethylamine near 0.25 M, the percent ionization is around 4.6 to 4.8 percent depending on the exact constants and concentration convention. That means the shortcut is borderline but generally acceptable for quick work, while the quadratic solution is preferred for a more exact answer.

Initial ethylamine concentration, M	Exact [OH-], M	Approximate pH at 25 C	Percent ionization
0.050	0.00502	11.70	10.0%
0.100	0.00721	11.86	7.21%
0.250	0.01157	12.06	4.63%
0.500	0.01647	12.22	3.29%
1.000	0.02339	12.37	2.34%

Common mistakes when calculating the pH of ethylamine solution

• Using K_a instead of K_b. Ethylamine is a base, so use K_b.
• Forgetting to solve for hydroxide first. The equilibrium gives [OH^–], not [H⁺].
• Confusing molality and molarity without stating the assumption.
• Applying the approximation without checking whether x is actually small relative to C.
• Rounding too early. Carry extra digits until the final pH.

What the final answer means chemically

A pH near 12.06 indicates a distinctly basic solution. This means ethylamine reacts with water enough to generate a measurable hydroxide concentration, but not so completely that it behaves like a strong base such as sodium hydroxide. Most ethylamine molecules remain unprotonated at equilibrium, and only a modest fraction convert into ethylammonium. In practical laboratory terms, such a solution can be irritating and chemically reactive, and it should be handled with proper safety precautions.

Recommended authoritative references

For supporting data and general acid base concepts, consult these sources:

• NIST Chemistry WebBook entry for ethylamine
• PubChem compound summary for ethylamine from NIH
• USGS overview of pH and water chemistry

Final takeaway

To calculate the pH of a 0.25 m solution of ethylamine, model ethylamine as a weak base in water, apply the K_b expression, solve for hydroxide concentration, then convert to pOH and pH. If you treat 0.25 m as effectively 0.247 to 0.250 M and use K_b ≈ 5.6 × 10^-4, the result is a pH of about 12.06. That value is robust across the exact and approximate methods, and it matches the expected behavior of a moderately strong weak base.

Calculator note: this tool uses a density based molality to molarity conversion when you select molality. For most dilute aqueous educational problems, the difference between 0.25 m and 0.25 M is small, but the calculator lets you see the more careful treatment.