Calculate The Ph Of A 0.045 M C2H5 2Nh Solution

Use this premium weak-base calculator to find the exact pH, pOH, hydroxide concentration, protonated amine concentration, and percent ionization for a diethylamine solution. The default setup matches the target problem: a 0.045 M solution of diethylamine, written here as C2H5 2NH and interpreted chemically as (C2H5)2NH.

Core chemistry

(C2H5)2NH + H2O ⇌ (C2H5)2NH2+ + OH-

For diethylamine at 25 C, a commonly used base dissociation constant is Kb = 9.6 × 10^-4.

Weak Base Calculator

• Equilibrium: B + H2O ⇌ BH+ + OH-
• Kb expression: Kb = [BH+][OH-] / [B]
• Exact equation: x² / (C – x) = Kb
• pOH: -log10[OH-]
• pH: pKw – pOH

How to Calculate the pH of a 0.045 M C2H5 2NH Solution

To calculate the pH of a 0.045 M C2H5 2NH solution, you first identify the solute as diethylamine, usually written more explicitly as (C2H5)2NH. Diethylamine is a weak base, which means it does not react completely with water. Instead, it establishes an equilibrium in which only a fraction of the dissolved base accepts a proton from water to produce hydroxide ions. Because pH depends on hydrogen ion concentration, and hydroxide ions are related to hydrogen ions through water autoionization, the calculation must proceed through base equilibrium chemistry.

The key reaction is:

(C2H5)2NH + H2O ⇌ (C2H5)2NH2+ + OH-

This reaction shows that every hydroxide ion formed comes from one molecule of diethylamine becoming protonated. For a weak base, the important equilibrium constant is Kb, the base dissociation constant. A typical textbook value for diethylamine near room temperature is Kb = 9.6 × 10^-4. Since this value is much less than 1, the reaction is only partial, but it is still strong enough that the resulting solution is definitely basic.

Step 1: Set up the ICE table

Let the initial concentration of diethylamine be C = 0.045 M. If x mol/L reacts with water, then equilibrium concentrations become:

• [(C2H5)2NH] = 0.045 – x
• [(C2H5)2NH2+] = x
• [OH-] = x

Substitute these into the expression for the base dissociation constant:

Kb = x² / (0.045 – x)

Now insert the known value of Kb:

9.6 × 10^-4 = x² / (0.045 – x)

Step 2: Solve the equilibrium expression

Many introductory chemistry problems use the approximation 0.045 – x ≈ 0.045 when x is very small. Here, that shortcut gives a reasonably close answer, but because the concentration is moderate and Kb is not extremely tiny, the exact quadratic solution is more rigorous and slightly more accurate.

Rearranging:

x² + Kb x – KbC = 0

Using the positive root of the quadratic formula:

x = [-Kb + √(Kb² + 4KbC)] / 2

Plugging in Kb = 9.6 × 10^-4 and C = 0.045 gives:

x ≈ 0.00612 M

Since x equals the hydroxide ion concentration, we have:

[OH-] ≈ 6.12 × 10^-3 M

Step 3: Convert hydroxide concentration to pOH and pH

The pOH is:

pOH = -log10(6.12 × 10^-3) ≈ 2.21

At 25 C, pH + pOH = 14.00, so:

pH = 14.00 – 2.21 = 11.79

Therefore, the pH of a 0.045 M diethylamine solution is about 11.79 when calculated exactly with Kb = 9.6 × 10^-4 at 25 C.

Final answer: For a 0.045 M solution of diethylamine, the expected pH is approximately 11.79. If you use the square-root approximation instead of the quadratic formula, you will get a very similar answer, typically around 11.82, depending on the Kb value and rounding.

Why Diethylamine Is Basic

Diethylamine is a secondary amine. The nitrogen atom has a lone pair that can accept a proton from water, making the molecule a Brønsted-Lowry base. The two ethyl groups attached to nitrogen tend to push electron density toward the nitrogen atom, which generally increases basicity relative to ammonia. In aqueous solution, this electronic effect helps diethylamine generate more hydroxide than a weaker base would at the same concentration.

This is why the pH is well above 7, yet not as high as a strong base such as sodium hydroxide. A strong base dissociates essentially completely, while diethylamine only partially reacts. That distinction is exactly why the weak-base equilibrium approach is needed.

When the Approximation Works and When It Does Not

Students are often taught the shortcut:

x ≈ √(Kb × C)

For this problem:

x ≈ √[(9.6 × 10^-4)(0.045)] ≈ 0.00657 M

Then:

• pOH ≈ 2.18
• pH ≈ 11.82

That estimate is close, but the exact method gives a slightly lower hydroxide concentration because the denominator is really 0.045 – x, not simply 0.045. In general, the approximation is best when the ionization is small compared with the initial concentration, often under the familiar 5 percent rule. In this case, ionization is significant enough that the exact solution is preferred if accuracy matters.

Common Weak Base Data for Comparison

It helps to compare diethylamine with other amines and with ammonia. The table below lists representative base dissociation constants at approximately 25 C. Exact values vary slightly by source and ionic strength, but these figures are standard enough for classroom calculations and general analytical work.

Base	Formula	Approx. Kb at 25 C	Approx. pKb	Relative Basicity in Water
Ammonia	NH3	1.8 × 10^-5	4.74	Lower than diethylamine
Methylamine	CH3NH2	4.4 × 10^-4	3.36	Moderately strong weak base
Ethylamine	C2H5NH2	5.6 × 10^-4	3.25	Stronger than methylamine
Diethylamine	(C2H5)2NH	9.6 × 10^-4	3.02	Strong among common simple amines
Aniline	C6H5NH2	4.3 × 10^-10	9.37	Much weaker due to resonance effects

The comparison shows why a 0.045 M diethylamine solution lands in the high-11 pH range. Its Kb is over 50 times larger than that of ammonia. At equal concentration, diethylamine therefore generates substantially more hydroxide ions.

Temperature Matters More Than Many Students Expect

In many classroom problems, the assumption is 25 C, so chemists use pKw = 14.00. But pKw changes with temperature, meaning the exact relationship between pH and pOH changes too. If the base equilibrium constant also changes with temperature, the final pH can shift for two reasons at once: one because of pKw, and another because of altered base strength.

Temperature	Approx. pKw	Neutral pH	What it Means for Basic Solutions
10 C	14.27	7.14	For the same pOH, calculated pH is slightly higher
25 C	14.00	7.00	Standard textbook condition
40 C	13.60	6.80	For the same pOH, calculated pH is slightly lower

This is why advanced pH calculators sometimes ask for temperature. In a precise laboratory setting, especially in analytical chemistry, environmental chemistry, or process chemistry, a difference of a few tenths of a pH unit may matter.

Step-by-Step Summary You Can Reuse

1. Identify the solute as a weak base, here diethylamine.
2. Write the equilibrium reaction with water.
3. Use an ICE table to define equilibrium concentrations.
4. Insert values into Kb = [BH+][OH-]/[B].
5. Solve for x = [OH-] using the approximation or the quadratic formula.
6. Calculate pOH = -log10[OH-].
7. Convert to pH with pH = pKw – pOH.

Most Common Mistakes in This Problem

• Confusing Kb with Ka: Since diethylamine is a base, you must use Kb unless you are given the conjugate acid Ka and intentionally convert it.
• Assuming complete dissociation: Weak bases do not fully ionize like NaOH.
• Forgetting the quadratic: If percent ionization is not tiny, the exact solution is better.
• Using pH = -log[OH-]: That gives pOH, not pH.
• Ignoring temperature: The relation pH + pOH = 14.00 is strictly true only at 25 C under standard assumptions.

Why the Percent Ionization Is Useful

Another meaningful quantity is the percent ionization:

% ionization = (x / C) × 100

Using the exact result, this is:

(0.00612 / 0.045) × 100 ≈ 13.6%

This confirms that the ionization is not negligible. A value above 5 percent tells you the shortcut approximation is starting to become less ideal, even though it still gives a close rough answer.

How This Calculator Interprets “C2H5 2NH”

The phrase C2H5 2NH is commonly intended to represent (C2H5)2NH, which is diethylamine. Without parentheses, chemical formulas can look ambiguous in plain text, but in acid-base calculations the intended meaning is usually clear from context. If you are working from a worksheet, textbook, or online prompt, the species is almost certainly diethylamine unless your instructor states otherwise.

Authoritative Chemistry References

For deeper reference reading, consult these authoritative sources:

• NIST Chemistry WebBook: Diethylamine data
• Beloit College chemistry resource on weak bases
• Florida State University acid-base concepts overview

Bottom Line

If you need to calculate the pH of a 0.045 M C2H5 2NH solution, the scientifically sound route is to treat the compound as diethylamine, use its weak-base equilibrium constant, solve for hydroxide concentration, then convert to pOH and pH. With Kb = 9.6 × 10^-4 at 25 C, the exact pH is approximately 11.79. That result fits the chemistry: diethylamine is clearly basic, stronger than ammonia, but still not fully dissociated like a strong base.

Use the calculator above to reproduce the default answer instantly, compare exact and approximate methods, or test how changes in concentration, Kb, and temperature influence the final pH.