Calculate the pH of 0.225 M Diethylamine Chloride
This interactive calculator determines the pH of a diethylamine chloride solution by treating diethylammonium chloride as the conjugate acid of the weak base diethylamine. Adjust concentration, pKb, and method to see how the result changes.
Diethylamine Chloride pH Calculator
Diethylamine + H+ ⇌ Diethylammonium+
pKa = 14.00 – pKb
Ka = 10-pKa
For concentration C of diethylammonium chloride:
Ka = x2 / (C – x), where x = [H+]
Concentration vs pH Trend
This chart compares the expected pH of diethylamine chloride over a practical concentration range using the selected pKb value. The highlighted point includes the 0.225 M case.
How to Calculate the pH of 0.225 M Diethylamine Chloride
If you need to calculate the pH of 0.225 M diethylamine chloride, the key idea is that this salt behaves as an acidic salt in water. Diethylamine itself is a weak base, and when it is protonated it becomes the diethylammonium ion. In diethylamine chloride, the chemically active species for acid-base behavior is the diethylammonium cation, while chloride is essentially a spectator ion in this context.
That means you do not solve this as a strong acid and you do not treat it as a neutral salt. Instead, you recognize that the solution contains the conjugate acid of a weak base. Once you identify that relationship, the rest of the calculation follows a standard weak acid equilibrium pathway.
Why diethylamine chloride is acidic in water
Diethylamine is a weak base, often written as (C2H5)2NH. Its protonated form is diethylammonium, (C2H5)2NH2+. When paired with chloride, the full salt dissociates in water like this:
(C2H5)2NH2Cl → (C2H5)2NH2+ + Cl–
The chloride ion comes from a strong acid, hydrochloric acid, so it does not significantly affect pH. The diethylammonium ion, however, can donate a proton to water:
(C2H5)2NH2+ + H2O ⇌ (C2H5)2NH + H3O+
Because hydronium is produced, the solution is acidic. That is why the pH falls below 7.
Step by step method
- Identify the acid-base type. Diethylamine chloride is a salt of a weak base and a strong acid. Therefore the solution is acidic because of the conjugate acid, diethylammonium.
- Use the base constant of diethylamine. A common value is pKb = 2.89 at 25 C.
- Convert pKb to pKa. For conjugate pairs at 25 C, pKa + pKb = 14.00. So pKa = 14.00 – 2.89 = 11.11.
- Convert pKa to Ka. Ka = 10-11.11 ≈ 7.76 × 10-12.
- Set up the equilibrium. For a 0.225 M solution of diethylammonium, let x = [H+]. Then Ka = x2 / (0.225 – x).
- Solve for x. Because Ka is very small, x is much smaller than 0.225, so x ≈ √(Ka × C) = √((7.76 × 10-12)(0.225)) ≈ 1.32 × 10-6 M.
- Calculate pH. pH = -log(1.32 × 10-6) ≈ 5.88.
Full numerical calculation for 0.225 M
Let the initial concentration of diethylammonium ion be 0.225 M. The equilibrium table is:
- Initial: [BH+] = 0.225, [B] = 0, [H+] = 0
- Change: [BH+] = -x, [B] = +x, [H+] = +x
- Equilibrium: [BH+] = 0.225 – x, [B] = x, [H+] = x
Substitute into the acid dissociation expression:
Ka = x2 / (0.225 – x)
Using Ka = 7.76 × 10-12, the exact quadratic gives:
x = [-Ka + √(Ka2 + 4KaC)] / 2
This yields essentially the same result as the weak acid approximation:
x ≈ 1.32 × 10-6 M
Then:
pH = -log(1.32 × 10-6) = 5.88
How reliable is the approximation?
For weak acids and conjugate acids of weak bases, the square root approximation is usually valid if the amount dissociated is much less than 5 percent of the initial concentration. Here, the percent ionization is extremely small:
(1.32 × 10-6 / 0.225) × 100 ≈ 0.00059%
That is far below 5 percent, so the approximation is excellent. In practice, the exact quadratic and the approximation agree to several meaningful digits for this case.
Comparison data for weak base and conjugate acid properties
The acid strength of diethylammonium is directly tied to the base strength of diethylamine. The table below summarizes the values used in this calculator and contrasts them with two other common amines often discussed in introductory acid-base chemistry.
| Base | Approx. pKb at 25 C | Approx. Kb | Conjugate acid pKa | Interpretation |
|---|---|---|---|---|
| Ammonia | 4.75 | 1.8 × 10-5 | 9.25 | Weaker base than diethylamine |
| Methylamine | 3.36 | 4.4 × 10-4 | 10.64 | Stronger base than ammonia |
| Diethylamine | 2.89 | 1.29 × 10-3 | 11.11 | Relatively strong weak base |
Because diethylamine is a stronger weak base than ammonia, its conjugate acid is weaker than ammonium. That is why diethylamine chloride is acidic, but not strongly acidic. A 0.225 M solution lands in the mildly acidic region rather than near the pH values you would expect from a strong acid such as hydrochloric acid.
How concentration changes the pH
Concentration matters. If everything else is held constant and only the molarity changes, the pH shifts according to the weak acid relationship. Higher concentration produces a slightly lower pH because more diethylammonium ions are present to donate protons. The change is not linear, though, because the equilibrium depends on the square root of concentration.
| Diethylamine chloride concentration (M) | Calculated [H+] (M) | Calculated pH | Percent ionization |
|---|---|---|---|
| 0.010 | 2.79 × 10-7 | 6.55 | 0.00279% |
| 0.050 | 6.23 × 10-7 | 6.21 | 0.00125% |
| 0.100 | 8.81 × 10-7 | 6.05 | 0.00088% |
| 0.225 | 1.32 × 10-6 | 5.88 | 0.00059% |
| 0.500 | 1.97 × 10-6 | 5.71 | 0.00039% |
Common mistakes students make
- Treating the salt as neutral. This is wrong because the cation is the conjugate acid of a weak base.
- Using Kb directly instead of Ka. Once the protonated amine is in solution, you need the acid dissociation constant of the conjugate acid.
- Forgetting pKa + pKb = 14.00 at 25 C. This relation is essential for converting the basicity data into acidity data.
- Using the chloride ion in the equilibrium. Chloride is a spectator here and does not control the pH.
- Assuming strong acid behavior. Even at 0.225 M, the solution is only mildly acidic because the acid is weak.
Practical interpretation of the result
A pH of roughly 5.88 means the solution is acidic, but not harshly so. For comparison, pure water at room temperature is near pH 7, many natural waters range around pH 6.5 to 8.5, and many laboratory weak acid solutions fall into the pH 4 to 6 range depending on concentration and acid strength. Diethylamine chloride at 0.225 M sits in a region consistent with a weakly acidic ammonium-type salt.
This matters in synthesis and analytical chemistry. Protonated amines are common in purification steps, salt formation, and pH control. If you are planning a buffer, extraction, or titration involving diethylamine or its hydrochloride salt, estimating the pH correctly helps you predict protonation state, solubility, and reaction behavior.
Authority sources for acid-base reference concepts
For readers who want official or academic reference material on pH, aqueous equilibria, and weak acid-base behavior, these sources are useful:
Summary
To calculate the pH of 0.225 M diethylamine chloride, treat the salt as a source of the weak acid diethylammonium. Start with the pKb of diethylamine, convert it to pKa for the conjugate acid, calculate Ka, and solve the weak acid equilibrium. With pKb = 2.89 at 25 C, the result is a hydrogen ion concentration of about 1.32 × 10-6 M and a pH of about 5.88.
If you use the calculator above, you can also explore how the pH changes with different concentrations or slightly different literature pKb values. For the standard textbook version of the problem, though, the answer most instructors expect is: