Calculate the pH of 0.10 M Dimethylamine
Use this interactive weak-base calculator to find the pH, pOH, hydroxide concentration, percent ionization, and equilibrium concentration for an aqueous dimethylamine solution. The default values are set to the classic chemistry problem of 0.10 M dimethylamine at 25 C using a literature Kb near 5.4 x 10-4.
Results
Click Calculate pH to solve the dimethylamine equilibrium.
How to calculate the pH of 0.10 M dimethylamine
Dimethylamine, written as (CH3)2NH, is a weak Bransted base. That means it does not react completely with water. Instead, it establishes an equilibrium:
(CH3)2NH + H2O ⇄ (CH3)2NH2+ + OH–
To calculate the pH of a 0.10 M dimethylamine solution, you need the initial concentration of the base and its base dissociation constant, Kb. A commonly used Kb value for dimethylamine at 25 C is about 5.4 x 10-4. Because the compound is a weak base rather than a strong base, you cannot assume that the initial concentration equals the hydroxide concentration. Instead, you must use an equilibrium expression and solve for the amount that ionizes.
Step 1: Write the Kb expression
Let x represent the equilibrium concentration of OH– produced. Then the ICE table gives:
- Initial dimethylamine concentration = 0.10 M
- Change in dimethylamine concentration = -x
- Equilibrium dimethylamine concentration = 0.10 – x
- Equilibrium hydroxide concentration = x
- Equilibrium dimethylammonium concentration = x
The Kb expression becomes:
Kb = x2 / (0.10 – x)
Substituting Kb = 5.4 x 10-4:
5.4 x 10-4 = x2 / (0.10 – x)
Step 2: Solve for x
There are two standard ways to solve weak base problems. The first is the approximation method, where you assume x is small compared with the initial concentration. The second is the exact quadratic method. For this problem, both approaches give very similar results, but the exact method is more rigorous and is what this calculator uses by default.
- Multiply both sides by (0.10 – x).
- Rearrange into a quadratic equation.
- Solve for the positive root, since concentration cannot be negative.
Using the exact solution, the hydroxide concentration is approximately 0.00708 M. That means:
- [OH–] ≈ 7.08 x 10-3 M
- pOH ≈ 2.15
- pH ≈ 11.85 at 25 C
So the pH of 0.10 M dimethylamine is about 11.85 when Kb is taken as 5.4 x 10-4 and pKw is 14.00.
Why dimethylamine gives a basic solution
Dimethylamine contains a nitrogen atom with a lone pair of electrons. That lone pair can accept a proton from water, producing the conjugate acid dimethylammonium and hydroxide ions. The hydroxide ions are what raise the pH above 7. Even though dimethylamine is a weak base, it is still substantially basic because its Kb is much larger than that of water and larger than the Kb of many other common weak bases used in introductory chemistry examples.
The value of Kb tells you how strongly the base reacts with water. A larger Kb means more OH– forms, giving a higher pH for the same starting concentration. Dimethylamine is stronger as a base than ammonia, which is why a 0.10 M dimethylamine solution has a higher pH than a 0.10 M ammonia solution.
Exact result vs approximate result
Students often learn the square root approximation:
x ≈ √(Kb x C)
For 0.10 M dimethylamine:
x ≈ √(5.4 x 10-4 x 0.10) = √(5.4 x 10-5) ≈ 7.35 x 10-3 M
This gives a pH very close to the exact answer. However, the approximation slightly overestimates the hydroxide concentration because it ignores the subtraction of x from the initial concentration. In general, if x is less than 5 percent of the initial concentration, the approximation is usually acceptable. Here, x is around 7 percent of 0.10 M, so the exact quadratic method is the better choice.
| Method | [OH-] at equilibrium | pOH | pH at 25 C | Comment |
|---|---|---|---|---|
| Exact quadratic | 7.08 x 10-3 M | 2.15 | 11.85 | Best for reporting a final answer |
| Approximate square root | 7.35 x 10-3 M | 2.13 | 11.87 | Fast estimate, slightly high |
Worked chemistry interpretation
The most useful way to interpret the answer is not just to state pH = 11.85, but to connect that number to the chemistry of the solution. A pH of 11.85 means the solution is distinctly basic and contains far more hydroxide than pure water. Pure water at 25 C has [OH–] = 1.0 x 10-7 M, while the dimethylamine solution has an [OH–] on the order of 10-3 M. That is roughly ten thousand times more hydroxide than pH 10 water and about seventy thousand times more hydroxide than neutral water. This helps explain why aqueous amines can significantly change acid-base behavior in reaction mixtures, extractions, buffers, and industrial formulations.
Another helpful quantity is the percent ionization. For this case:
Percent ionization = (x / 0.10) x 100 ≈ 7.08%
This confirms that dimethylamine is weak, because most of the molecules remain unprotonated at equilibrium, but it is not so weak that ionization is negligible. In a 0.10 M solution, about 92.92 percent remains as dimethylamine and about 7.08 percent has accepted a proton from water.
Comparison with other common weak bases
One of the best ways to understand the pH of dimethylamine is to compare it with other weak bases studied in general chemistry. The table below uses representative 25 C base dissociation constants and shows approximate exact pH values for 0.10 M solutions. These values illustrate how strongly the equilibrium constant influences the final pH.
| Base | Representative Kb at 25 C | Approximate pH for 0.10 M solution | Relative basic strength |
|---|---|---|---|
| Ammonia, NH3 | 1.8 x 10-5 | 11.13 | Weaker than dimethylamine |
| Methylamine, CH3NH2 | 4.4 x 10-4 | 11.81 | Slightly weaker than dimethylamine |
| Dimethylamine, (CH3)2NH | 5.4 x 10-4 | 11.85 | Stronger than ammonia and methylamine |
| Trimethylamine, (CH3)3N | 6.3 x 10-5 | 11.38 | Weaker than dimethylamine |
Common mistakes when solving this problem
1. Treating dimethylamine like a strong base
If you incorrectly assume all 0.10 M dimethylamine becomes OH–, you would calculate pOH = 1 and pH = 13. That is much too high. Weak bases only partially ionize.
2. Using Ka instead of Kb
Dimethylamine is a base, so you should use Kb directly. If you are given the pKa of the conjugate acid dimethylammonium instead, convert carefully using pKa + pKb = pKw at the chosen temperature.
3. Forgetting that pH and pOH depend on temperature
The familiar relation pH + pOH = 14.00 is true at 25 C. If the problem specifies another temperature, use the proper pKw value. This calculator lets you change that assumption.
4. Reporting too many significant figures
Since the concentration is given as 0.10 M and Kb is often quoted to two significant figures, a final pH of 11.85 is typically a sensible level of precision for classroom and practical calculations.
When the Henderson-Hasselbalch style approach applies
For a pure dimethylamine solution, you generally solve with the weak base equilibrium expression. If the system also contains a substantial amount of dimethylammonium salt, then you have a buffer and can use a pOH form of the Henderson-Hasselbalch equation or its pH equivalent after converting through the conjugate acid. In that situation, the pH depends on the ratio of base to conjugate acid rather than only on the initial base concentration.
Practical significance of dimethylamine pH calculations
Dimethylamine appears in synthetic chemistry, industrial processing, analytical chemistry, and environmental systems. Knowing its pH behavior matters when predicting reaction pathways, setting extraction conditions, controlling corrosion, or estimating how nitrogen-containing organics behave in water. In laboratory work, pH calculations help determine whether an amine is mostly protonated or unprotonated, which in turn affects solubility, volatility, and reactivity.
For example, in an acidic medium dimethylamine is converted largely into dimethylammonium, which is more water-soluble and less nucleophilic than the free base. In a basic medium, more of the neutral amine remains present. This distinction is especially important in separations, acid-base extractions, and catalysis.
Authoritative references for deeper study
If you want to verify acid-base conventions, aqueous pH definitions, and chemical property information, these sources are useful:
- U.S. Environmental Protection Agency on pH fundamentals
- NIST Chemistry WebBook entry for dimethylamine
- University of Wisconsin acid-base equilibrium tutorial
Final answer summary
To calculate the pH of 0.10 M dimethylamine, write the weak-base equilibrium, use Kb = 5.4 x 10-4, solve for the hydroxide concentration, then convert to pOH and pH. The exact quadratic solution gives [OH–] ≈ 7.08 x 10-3 M, pOH ≈ 2.15, and pH ≈ 11.85 at 25 C.