Calculate the pH of a 0.14 M Solution of Diethylamine
Use this premium chemistry calculator to determine the pH, pOH, hydroxide concentration, and conjugate acid concentration for an aqueous diethylamine solution. The default setup is 0.14 M diethylamine at 25 degrees Celsius with a standard literature Kb value, but you can adjust the inputs for study, lab checking, and exam practice.
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Equilibrium Visualization
This chart compares the starting diethylamine concentration with the equilibrium concentrations of unreacted base, hydroxide ion, and diethylammonium ion after the weak-base reaction reaches equilibrium.
How to calculate the pH of a 0.14 M solution of diethylamine
To calculate the pH of a 0.14 M solution of diethylamine, you treat diethylamine as a weak Brønsted base. Unlike a strong base such as sodium hydroxide, diethylamine does not ionize completely in water. Instead, only a fraction of the dissolved molecules accept a proton from water and generate hydroxide ions. That equilibrium behavior is the key reason this problem requires a weak-base calculation rather than a direct concentration-to-pH conversion.
Diethylamine, often written as (C2H5)2NH, reacts with water according to this equilibrium:
The equilibrium is described by the base dissociation constant, Kb. A commonly used room-temperature value for diethylamine is approximately 9.6 × 10-4, although exact values can differ slightly among references and temperatures. Once you know the initial concentration and Kb, the path to pH is straightforward: solve for hydroxide concentration, compute pOH, and then convert pOH to pH.
Step-by-step setup
- Write the balanced weak-base reaction in water.
- Set up an ICE table: Initial, Change, Equilibrium.
- Let x equal the hydroxide concentration formed at equilibrium.
- Substitute into the Kb expression.
- Solve for x exactly with the quadratic formula or approximately with the weak-base shortcut.
- Use pOH = -log[OH–].
- Use pH = 14.00 – pOH at 25 degrees Celsius.
ICE table for 0.14 M diethylamine
If the starting concentration is 0.14 M and no hydroxide or conjugate acid is added initially, the ICE table becomes:
- Initial: [Base] = 0.14, [BH+] = 0, [OH–] = 0
- Change: [Base] = -x, [BH+] = +x, [OH–] = +x
- Equilibrium: [Base] = 0.14 – x, [BH+] = x, [OH–] = x
The base dissociation expression is:
Using Kb = 9.6 × 10-4:
You can solve this exactly:
x2 + (9.6 × 10-4)x – (1.344 × 10-4) = 0
The physically meaningful root gives x ≈ 0.01112 M. Since x is the hydroxide concentration, [OH–] ≈ 0.01112 M.
Now calculate pOH:
pOH = -log(0.01112) ≈ 1.954
Then convert to pH:
pH = 14.00 – 1.954 = 12.046
Why this pH is basic but not as high as a strong base
Students often wonder why 0.14 M diethylamine does not produce a pH as high as 0.14 M sodium hydroxide. The reason is dissociation strength. Sodium hydroxide dissociates essentially completely, so the hydroxide concentration is nearly 0.14 M. Diethylamine is weak, so only a modest fraction converts into hydroxide ions. That partial proton-accepting behavior lowers the final [OH–] and therefore lowers the pH relative to a strong base of equal formal concentration.
| Solution | Formal concentration | Assumed dissociation behavior | Approximate [OH–] | Approximate pH at 25 degrees Celsius |
|---|---|---|---|---|
| Diethylamine | 0.14 M | Weak base, partial reaction with water | 0.0111 M | 12.05 |
| Sodium hydroxide | 0.14 M | Strong base, nearly complete dissociation | 0.14 M | 13.15 |
This comparison makes the chemistry intuitive. Both solutions start at the same formal molarity, but their proton-accepting power in water differs greatly because one is weak and one is strong. Therefore, molarity alone never tells the full pH story for weak electrolytes.
Approximation method versus exact quadratic method
For many weak acid and weak base problems, chemists use the approximation:
x ≈ √(Kb × C)
Here, C is the initial base concentration. For diethylamine:
x ≈ √[(9.6 × 10-4)(0.14)] = √(1.344 × 10-4) ≈ 0.01159 M
This gives a pOH around 1.936 and a pH around 12.064. That is very close to the exact quadratic answer. The difference is small because x is still much smaller than the starting concentration, although not tiny. If you need the most defensible answer for lab work, graded homework, or a chemistry calculator, the exact quadratic solution is better.
| Method | Equation used | [OH–] result | pH result | Comment |
|---|---|---|---|---|
| Exact quadratic | x = [-Kb + √(Kb2 + 4KbC)] / 2 | 0.01112 M | 12.046 | Best for calculator-grade accuracy |
| Approximation | x ≈ √(KbC) | 0.01159 M | 12.064 | Fast and usually acceptable in classwork |
What does the percent ionization tell you?
Another useful quantity is the percent ionization, which tells you what fraction of the original diethylamine actually reacts with water. It is calculated as:
Percent ionization = ([OH–] / initial concentration) × 100
Using the exact result:
(0.01112 / 0.14) × 100 ≈ 7.94%
That means just under 8% of the diethylamine molecules are protonated at equilibrium under these conditions. This is entirely consistent with weak-base behavior: noticeable ionization, but far from complete dissociation.
Common mistakes when solving this problem
- Using pH = -log(0.14): this is wrong because 0.14 M is the base concentration, not the hydrogen ion concentration.
- Treating diethylamine as a strong base: weak bases require an equilibrium calculation.
- Forgetting to calculate pOH first: bases produce hydroxide, so you usually find pOH before converting to pH.
- Using Ka instead of Kb: diethylamine is a base, so Kb is the relevant constant unless you convert from the conjugate acid data.
- Ignoring temperature: pH and equilibrium constants vary with temperature, although 25 degrees Celsius is standard for textbook problems.
How concentration affects the pH of diethylamine solutions
As the formal concentration of diethylamine increases, the hydroxide concentration also rises, but not in a perfectly linear way because the system is controlled by equilibrium. Weak bases tend to show a pH increase with concentration, but the exact change depends on both the concentration and Kb. The stronger the base, the more readily it forms hydroxide ions.
Below are representative values using Kb = 9.6 × 10-4 and the exact weak-base equation:
| Diethylamine concentration | Calculated [OH–] | pOH | pH |
|---|---|---|---|
| 0.010 M | 0.00266 M | 2.575 | 11.425 |
| 0.050 M | 0.00646 M | 2.190 | 11.810 |
| 0.140 M | 0.01112 M | 1.954 | 12.046 |
| 0.500 M | 0.02146 M | 1.668 | 12.332 |
This trend shows why concentration matters, but also why weak-base calculations are not the same as strong-base calculations. Even at 0.500 M, the pH is still far below what a 0.500 M strong base would generate.
Real-world context for diethylamine in chemistry
Diethylamine is an organic amine and a common example in acid-base chemistry because it is basic, water-reactive, and structurally simple enough to illustrate weak-base equilibrium behavior. Organic amines are relevant in synthesis, pharmaceuticals, analytical chemistry, and industrial processes. In introductory and general chemistry, they also serve as a bridge between pure equilibrium mathematics and real molecular behavior.
Because diethylamine has an alkyl-substituted nitrogen, it has greater electron density at nitrogen than ammonia, which tends to increase basicity in aqueous solution. That is one reason amines are often stronger bases than ammonia, although solvation and molecular structure can complicate exact comparisons.
Authoritative references and further reading
If you want to verify pH conventions, equilibrium fundamentals, and laboratory handling information, these references are useful:
- LibreTexts Chemistry for broad acid-base equilibrium explanations.
- U.S. Environmental Protection Agency for pH background, water chemistry context, and chemical information.
- NIST Chemistry WebBook for chemical property reference data.
- Occupational Safety and Health Administration for laboratory safety awareness involving amines and corrosive/basic materials.
- University chemistry resources for equilibrium and weak-base problem solving approaches.
Final takeaway
To calculate the pH of a 0.14 M solution of diethylamine, you must use weak-base equilibrium rather than assume complete ionization. Start with the reaction of diethylamine and water, define x as the hydroxide concentration formed, and solve the Kb expression. With Kb = 9.6 × 10-4, the exact calculation gives [OH–] ≈ 0.01112 M, pOH ≈ 1.954, and therefore pH ≈ 12.05.
That result is chemically sensible: diethylamine is basic enough to produce a strongly basic solution, but because it is still a weak base, the pH remains lower than that of an equally concentrated strong base. If you are studying for exams, checking homework, or building intuition in equilibrium chemistry, this is a classic and very useful problem type to master.