Calculate the pH of a 0.05 M C2H5 2NH Solution
Use this premium weak-base calculator to find hydroxide concentration, pOH, and pH for a diethylamine solution using either the exact quadratic solution or the standard approximation.
How to calculate the pH of a 0.05 M C2H5 2NH solution
When you need to calculate the pH of a 0.05 M C2H5 2NH solution, you are working with a weak base equilibrium problem. The formula written as C2H5 2NH usually refers to diethylamine, more precisely written as (C2H5)2NH. Diethylamine is an organic amine, and like many amines, it behaves as a weak Bronnsted-Lowry base in water. That means it does not ionize completely the way sodium hydroxide does. Instead, it reacts only partially with water to produce hydroxide ions:
The pH depends on how much hydroxide ion, OH-, is generated at equilibrium. Because the base is weak, you must use the base dissociation constant, Kb, rather than assuming full dissociation. For diethylamine, a commonly used room-temperature value is approximately 1.3 × 10^-3. This value can vary slightly between data compilations, but it is a sound default for most educational calculations.
Step 1: Write the equilibrium expression
For the reaction above, the base dissociation expression is:
If the initial concentration of diethylamine is 0.05 M, and if x is the amount that reacts, then the equilibrium concentrations become:
- [(C2H5)2NH] = 0.05 – x
- [(C2H5)2NH2+] = x
- [OH-] = x
Substitute these values into the equilibrium expression:
Step 2: Solve for hydroxide concentration
There are two common ways to solve this type of problem. The first is the approximation method, which assumes x is small compared with the initial concentration. The second is the exact quadratic method, which gives a more precise answer. For a weak base with Kb in the 10^-3 range and a starting concentration of 0.05 M, the approximation is usable, but the exact method is better because the ionization is not extremely tiny.
Using the approximation:
x^2 ≈ 6.5 × 10^-5
x ≈ 8.06 × 10^-3 M
So the hydroxide concentration is about 0.00806 M. If you solve exactly with the quadratic equation:
where C = 0.05 M and Kb = 0.0013, the value comes out very close to:
The exact result is slightly lower than the approximation because the denominator is really 0.05 – x, not simply 0.05. This difference matters more as the weak base becomes somewhat stronger or more concentrated.
Step 3: Convert [OH-] into pOH
Once you know hydroxide concentration, calculate pOH using:
Using the exact hydroxide concentration, 7.44 × 10^-3 M:
Step 4: Convert pOH into pH
At 25 C, pH and pOH are related by:
Therefore:
Final answer: the pH of a 0.05 M diethylamine solution is about 11.87 using Kb = 1.3 × 10^-3.
Why this solution is basic
Amines contain a nitrogen atom with a lone pair of electrons. That lone pair can accept a proton from water, producing the protonated amine and hydroxide ions. Since hydroxide ions increase in the solution, the pH rises above 7. In the case of diethylamine, two ethyl groups attached to nitrogen help stabilize the protonated form and make the amine a noticeably stronger base than ammonia.
Comparison with ammonia and stronger bases
Students often understand this problem better by comparing diethylamine to other familiar bases. Sodium hydroxide is a strong base and dissociates completely. Ammonia is a weak base with a lower Kb than diethylamine. Diethylamine sits in the middle ground: it is still a weak base because equilibrium is involved, but it is stronger than ammonia and generates more OH- at the same initial concentration.
| Base | Typical Kb at 25 C | Strength Category | Expected pH at 0.05 M |
|---|---|---|---|
| Ammonia, NH3 | 1.8 × 10^-5 | Weak base | About 10.48 |
| Diethylamine, (C2H5)2NH | 1.3 × 10^-3 | Weak base, stronger than ammonia | About 11.87 |
| Sodium hydroxide, NaOH | Essentially complete dissociation | Strong base | About 12.70 |
These comparison values show an important trend. Even though diethylamine is not a strong base, its pH at 0.05 M is significantly higher than that of ammonia because its Kb is much larger. However, it still does not reach the pH of a 0.05 M NaOH solution, because NaOH fully dissociates and produces 0.05 M hydroxide immediately.
Approximation method versus exact method
In many chemistry classes, instructors teach the shortcut:
This shortcut is excellent when x is less than 5 percent of the initial concentration. For diethylamine at 0.05 M:
- Approximate x ≈ 0.00806 M
- 5 percent of 0.05 M = 0.0025 M
Since 0.00806 M is clearly greater than 0.0025 M, the 5 percent rule is not fully satisfied. That means the approximation introduces noticeable error. The exact quadratic calculation is therefore the preferred route if you want a more defensible pH value.
| Method | [OH-] Found | pOH | pH | Comment |
|---|---|---|---|---|
| Approximation | 8.06 × 10^-3 M | 2.09 | 11.91 | Fast but slightly high |
| Quadratic exact | 7.44 × 10^-3 M | 2.13 | 11.87 | Best educational answer |
Common mistakes when calculating the pH of a diethylamine solution
- Treating diethylamine like a strong base. You should not assume [OH-] = 0.05 M.
- Using Ka instead of Kb. Amines are weak bases, so the natural equilibrium constant is Kb unless you are working through the conjugate acid.
- Forgetting to convert from pOH to pH. Weak base problems usually give [OH-] first, not [H3O+].
- Skipping the 5 percent check. If the approximation is not valid, the final pH can be off enough to matter on exams or lab reports.
- Using the wrong molecular identity. C2H5 2NH is shorthand for (C2H5)2NH, diethylamine, not ethylamine.
What the chemistry means in practical terms
A pH near 11.9 indicates a clearly basic solution. Such a solution is capable of neutralizing acids and can affect indicators, reaction rates, and solubility of various compounds. Organic amines like diethylamine are common in synthetic chemistry, pharmaceutical processing, separations, and analytical work. Knowing the pH helps chemists predict protonation state, buffer behavior, extraction efficiency, and safe handling requirements.
The result also shows why weak bases can still produce fairly high pH values when their Kb is large enough and concentration is moderate. Students often hear the phrase “weak base” and assume the pH will be only slightly above 7, but that is not necessarily true. Weak means incomplete reaction, not insignificant effect. Diethylamine demonstrates this well because 0.05 M is concentrated enough to produce substantial hydroxide even though equilibrium limits full ionization.
Quick summary procedure
- Identify C2H5 2NH as diethylamine, a weak base.
- Use the equilibrium reaction with water to generate OH-.
- Write the Kb expression and substitute initial concentration 0.05 M.
- Solve for x, the equilibrium hydroxide concentration.
- Compute pOH = -log[OH-].
- Compute pH = 14 – pOH.
Authoritative references for acid-base constants and pH concepts
For reliable chemistry data and foundational acid-base guidance, consult authoritative educational and government resources. Good starting points include the LibreTexts Chemistry library for worked equilibrium concepts, the U.S. Environmental Protection Agency for pH background and water chemistry context, and NIST Chemistry WebBook for high-quality chemical reference data. While constant values for specific amines may vary slightly by source and temperature, the methodology shown here remains the standard approach.
Final conclusion
To calculate the pH of a 0.05 M C2H5 2NH solution, treat the compound as weak base diethylamine, apply its Kb, solve for equilibrium hydroxide concentration, then convert to pOH and pH. Using Kb = 1.3 × 10^-3 and the exact quadratic method gives [OH-] ≈ 7.44 × 10^-3 M, pOH ≈ 2.13, and pH ≈ 11.87. That is the best concise answer for typical general chemistry work. If your course or source uses a slightly different Kb, the calculator above lets you update the constant instantly and see how the predicted pH changes.