Calculate the pH of a 0.050 M C2H5 2NH Solution
Use this premium weak-base calculator to find the pH, pOH, hydroxide concentration, conjugate acid concentration, and remaining base concentration for diethylamine, commonly written as (C2H5)2NH. The tool applies the equilibrium expression for a weak base and visualizes the result with a responsive chart.
Weak Base pH Calculator
Equilibrium expression: Kb = [BH+][OH–] / [B]
Quadratic setup: Kb = x2 / (C – x), where x = [OH–]
Results
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Click Calculate pH to compute the equilibrium values for the 0.050 M (C2H5)2NH solution.
How to calculate the pH of a 0.050 M C2H5 2NH solution
To calculate the pH of a 0.050 M C2H5 2NH solution, you first recognize that the formula refers to diethylamine, which is more precisely written as (C2H5)2NH. Diethylamine is a weak base, not a strong base, so it does not fully dissociate in water. That means you cannot simply assume the hydroxide concentration equals the initial base concentration. Instead, you must use the base dissociation constant, Kb, and solve the equilibrium expression.
At 25°C, a commonly cited Kb value for diethylamine is approximately 9.6 × 10-4. If the initial concentration is 0.050 M, the equilibrium in water is:
(C2H5)2NH + H2O ⇌ (C2H5)2NH2+ + OH–
Because diethylamine accepts a proton from water, it generates hydroxide ions and makes the solution basic. The main quantity you solve for is [OH–]. Once you know that, you can compute pOH from pOH = -log[OH–], and then compute pH using pH = 14.00 – pOH at 25°C.
Step-by-step solution for 0.050 M diethylamine
- Write the weak base equilibrium:
(C2H5)2NH + H2O ⇌ (C2H5)2NH2+ + OH– - Set the initial concentration of diethylamine to 0.050 M.
- Let x be the amount of base that reacts. Then at equilibrium:
- [OH–] = x
- [(C2H5)2NH2+] = x
- [(C2H5)2NH] = 0.050 – x
- Substitute into the Kb expression:
9.6 × 10-4 = x2 / (0.050 – x) - Solve the equation. Using the quadratic form gives:
x = [-Kb + √(Kb2 + 4KbC)] / 2 - Substitute Kb = 9.6 × 10-4 and C = 0.050:
x ≈ 0.00646 M - Calculate pOH:
pOH = -log(0.00646) ≈ 2.190 - Calculate pH:
pH = 14.00 – 2.190 = 11.810
So the pH of a 0.050 M diethylamine solution is approximately 11.81 when Kb = 9.6 × 10-4 at 25°C.
Why diethylamine is treated as a weak base
Students often make the mistake of treating amines as if they were strong bases like sodium hydroxide. That is not correct. Organic amines such as methylamine, ethylamine, dimethylamine, and diethylamine only partially react with water. Their basicity depends on how strongly the nitrogen atom can accept a proton and how stable the protonated form becomes in water.
Diethylamine contains two ethyl groups attached to nitrogen. These alkyl groups donate electron density to nitrogen, making the lone pair more available for protonation. As a result, diethylamine is a stronger base than ammonia. However, it still falls in the category of a weak base because the proton transfer to water does not go to completion.
When can you use the square root approximation?
Many chemistry problems use the approximation:
x ≈ √(KbC)
For this problem:
x ≈ √((9.6 × 10-4)(0.050)) = √(4.8 × 10-5) ≈ 0.00693 M
This gives:
- pOH ≈ 2.159
- pH ≈ 11.841
The approximation is close, but not exact. The difference here is modest, yet noticeable in a precise homework, lab, or exam context. Because x is not extremely small compared with the initial concentration, the quadratic approach is better. The percent ionization is roughly:
(0.00646 / 0.050) × 100 ≈ 12.9%
That is above the usual 5% guideline for safely applying the approximation without checking error, so the quadratic method is the more rigorous path.
Comparison of exact and approximate methods
| Method | [OH-] (M) | pOH | pH | Comment |
|---|---|---|---|---|
| Quadratic equilibrium solution | 0.00646 | 2.190 | 11.810 | Most accurate for this concentration and Kb |
| Square root approximation | 0.00693 | 2.159 | 11.841 | Slightly overestimates basicity |
| Difference | 0.00047 | 0.031 | 0.031 | Small but important in precision work |
Real comparison data for weak bases
One helpful way to understand the pH of diethylamine is to compare its Kb with the Kb values of other common weak bases. As Kb gets larger, the base generally produces more OH– at the same starting concentration, which leads to a higher pH.
| Base | Typical Kb at 25°C | Relative basicity trend | Estimated pH at 0.050 M |
|---|---|---|---|
| Ammonia, NH3 | 1.8 × 10-5 | Much weaker than diethylamine | About 10.98 |
| Methylamine, CH3NH2 | 4.4 × 10-4 | Strong weak base | About 11.61 |
| Diethylamine, (C2H5)2NH | 9.6 × 10-4 | Stronger weak base | About 11.81 |
| Dimethylamine, (CH3)2NH | 5.4 × 10-4 | Strong weak base | About 11.67 |
This comparison shows that a 0.050 M diethylamine solution is substantially more basic than a 0.050 M ammonia solution. The reason is the larger Kb. Since Kb quantifies the tendency of the base to react with water and form OH–, the higher Kb of diethylamine directly explains the higher pH.
ICE table setup for the problem
An ICE table is often the cleanest way to organize weak base equilibrium problems:
- Initial: [(C2H5)2NH] = 0.050, [(C2H5)2NH2+] = 0, [OH–] = 0
- Change: -x, +x, +x
- Equilibrium: 0.050 – x, x, x
Then place those values into:
Kb = x2 / (0.050 – x)
This same process works for many weak bases, including ammonia and organic amines. If your instructor has not yet introduced the quadratic formula, the approximation may be expected. If your instructor emphasizes exact equilibrium calculations, use the quadratic method.
Common mistakes when calculating the pH of diethylamine
- Using Ka instead of Kb. Diethylamine is a base, so use Kb or convert from pKb if needed.
- Assuming full dissociation. If you set [OH–] = 0.050 M directly, you would get pH ≈ 12.70, which is far too high for a weak base.
- Forgetting to convert from pOH to pH. Once you find [OH–], the first logarithmic result is pOH, not pH.
- Ignoring temperature. The familiar relation pH + pOH = 14.00 is standard at 25°C, but the value changes slightly with temperature.
- Applying the approximation without checking percent ionization. Here, the ionization is large enough that the exact method is safer.
How the pH changes if the concentration changes
If the concentration of diethylamine increases, the hydroxide concentration generally increases too, so the pH rises. However, because the base is weak, the pH does not rise in a perfectly linear way with concentration. Equilibrium behavior means the percent ionization often decreases as concentration becomes larger, even though the absolute OH– concentration rises.
For example, if you compare several diethylamine concentrations using the same Kb value:
- At 0.010 M, the pH is lower than at 0.050 M
- At 0.050 M, the pH is about 11.81
- At 0.100 M, the pH is a bit higher still, but not doubled in any direct way
This is why equilibrium chemistry is so important. Weak acids and weak bases rarely allow shortcut arithmetic beyond carefully justified approximations.
Authoritative chemistry references
If you want to verify weak base concepts, pH definitions, or acid-base equilibria from trusted educational and government sources, these references are useful:
- LibreTexts Chemistry
- United States Environmental Protection Agency
- Purdue University Department of Chemistry
Practical summary
To solve the problem “calculate the pH of a 0.050 M C2H5 2NH,” identify the compound as diethylamine, write the weak base equilibrium, use the Kb expression, solve for hydroxide concentration, find pOH, and finally convert to pH. Using Kb = 9.6 × 10-4 at 25°C gives an OH– concentration near 0.00646 M and a final pH of about 11.81.
This value makes chemical sense. The solution is clearly basic, but not as basic as a 0.050 M solution of a strong base such as NaOH. The difference comes from incomplete ionization, which is the defining feature of weak bases. If you remember that diethylamine is a weak base and not a fully dissociating one, the entire problem becomes a straightforward equilibrium calculation.