Real-world examples of determining pH of weak base solutions

Starting with concrete examples of determining pH of weak base solutions

Let’s skip the abstract theory and go straight into real examples of determining pH of weak base solutions, then connect the dots as we go.

We’ll focus on the classic weak base equilibrium:

\[ \text{B} + \text{H}_2\text{O} \rightleftharpoons \text{BH}^+ + \text{OH}^- \]

with the base dissociation constant:

\[ K_b = \frac{[\text{BH}^+][\text{OH}^-]}{[\text{B}]} \]

and the familiar relationships:

• \(pOH = -\log[\text{OH}^-]\)
• \(pH = 14.00 - pOH\) (at 25 °C)

We’ll build a set of real examples that mirror what you actually see in problem sets and exams.

Classic example of determining pH of a weak base: ammonia

Ammonia (NH₃) is the textbook weak base. It’s used in cleaners, fertilizers, and is a standard in chemistry courses. A very common example of determining pH of weak base solutions uses a 0.10 M NH₃ solution.

Data:

• Base: NH₃(aq)
• Reaction: \(\text{NH}_3 + \text{H}_2\text{O} \rightleftharpoons \text{NH}_4^+ + \text{OH}^-\)
• \(K_b(\text{NH}_3) \approx 1.8 \times 10^{-5}\) at 25 °C (see tables in standard general chemistry texts or NIST data).
• Initial \([\text{NH}_3] = 0.10\,\text{M}\)

Set up an ICE (Initial–Change–Equilibrium) table:

• Initial: \([\text{NH}_3] = 0.10\), \([\text{NH}_4^+] = 0\), \([\text{OH}^-] = 0\)
• Change: \(-x, +x, +x\)
• Equilibrium: \(0.10 - x, x, x\)

Plug into \(K_b\):

[
K_b = \frac{x \cdot x}{0.10 - x} = 1.8 \times 10^{-5}
]

Assume \(x \ll 0.10\), so \(0.10 - x \approx 0.10\):

[
1.8 \times 10^{-5} \approx \frac{x^2}{0.10}
]
[
x^2 \approx 1.8 \times 10^{-6}
]
[
x \approx 1.34 \times 10^{-3}\,\text{M} = [\text{OH}^-]
]

Now convert to pH:

[
pOH = -\log(1.34 \times 10^{-3}) \approx 2.87
]
[
pH = 14.00 - 2.87 = 11.13
]

This is one of the best examples for building intuition: a 0.10 M weak base gives a pH well above 7 but far below the pH of a 0.10 M strong base (which would be 13.00).

Check the approximation:

\(\frac{x}{0.10} = \frac{1.34 \times 10^{-3}}{0.10} = 0.0134\), or about 1.34%. That’s small enough that the approximation is fine.

More examples of determining pH of weak base solutions at different concentrations

To see how concentration affects pH, it helps to compare two or three examples using the same weak base. Here we’ll use ammonia again but change the molarity.

Example of 0.010 M NH₃ solution

Same \(K_b = 1.8 \times 10^{-5}\), but now \([\text{NH}_3]_0 = 0.010\,\text{M}\).

ICE table gives equilibrium \(0.010 - x, x, x\), and

[
1.8 \times 10^{-5} = \frac{x^2}{0.010 - x}
]

Approximate \(0.010 - x \approx 0.010\):

[
x^2 \approx 1.8 \times 10^{-7}
]
[
x \approx 4.24 \times 10^{-4}\,\text{M} = [\text{OH}^-]
]

Then:

[
pOH = -\log(4.24 \times 10^{-4}) \approx 3.37
]
[
pH = 14.00 - 3.37 = 10.63
]

Compared with 0.10 M NH₃ (pH ≈ 11.13), diluting by a factor of 10 drops the pH by about 0.5 units. This is a great real example of how weak base pH doesn’t scale linearly with concentration.

Example of very dilute NH₃: 1.0 × 10⁻⁵ M

Now the water autoionization starts to matter, and this is where students often trip up.

• \([\text{NH}_3]_0 = 1.0 \times 10^{-5}\,\text{M}\)
• \(K_b = 1.8 \times 10^{-5}\)

If you naïvely apply the same method:

[
K_b = \frac{x^2}{1.0 \times 10^{-5} - x}
]

you quickly see that \(x\) is not necessarily much smaller than \(1.0 \times 10^{-5}\). In fact, for very dilute weak bases, the \([\text{OH}^-]\) from water (\(1.0 \times 10^{-7}\,\text{M}\)) becomes comparable to what the base produces.

In many courses, instructors either:

• Avoid this concentration range, or
• Explicitly teach how to include water autoionization and solve a cubic or use numerical methods.

If you’re working at this level, check your textbook or online resources from universities like MIT OpenCourseWare or UC Davis ChemWiki (now LibreTexts) for detailed treatments.

The key takeaway from this example of determining pH of a weak base solution is conceptual: at very low base concentration, water’s own \(K_w\) contribution can no longer be ignored.

Examples include organic weak bases: methylamine and aniline

Not all weak bases are inorganic. Many biologically relevant molecules are weak bases. Two of the best examples of determining pH of weak base solutions in organic chemistry courses are methylamine and aniline.

Methylamine, CH₃NH₂, 0.20 M

Methylamine is a stronger base than ammonia.

Typical data:

• \(K_b(\text{CH}_3\text{NH}_2) \approx 4.4 \times 10^{-4}\)
• \([\text{CH}_3\text{NH}_2]_0 = 0.20\,\text{M}\)

Set up equilibrium:

• Initial: \(0.20, 0, 0\)
• Change: \(-x, +x, +x\)
• Equilibrium: \(0.20 - x, x, x\)

Equation:

[
4.4 \times 10^{-4} = \frac{x^2}{0.20 - x}
]

Approximate \(0.20 - x \approx 0.20\):

[
x^2 \approx 8.8 \times 10^{-5}
]
[
x \approx 9.38 \times 10^{-3}\,\text{M} = [\text{OH}^-]
]

Then:

[
pOH = -\log(9.38 \times 10^{-3}) \approx 2.03
]
[
pH = 14.00 - 2.03 = 11.97
]

This example shows how a larger \(K_b\) (stronger weak base) at similar concentration pushes pH closer to that of a strong base.

Check approximation:

\(x/0.20 \approx 0.00938/0.20 = 0.047\), about 4.7%. Borderline, but still often accepted in intro courses. If you want higher accuracy, use the quadratic formula instead of the approximation.

Aniline, C₆H₅NH₂, 0.10 M

Aniline is much weaker as a base than ammonia.

Typical data:

• \(K_b(\text{aniline}) \approx 4.3 \times 10^{-10}\)
• \([\text{aniline}]_0 = 0.10\,\text{M}\)

ICE table gives \(0.10 - x, x, x\) and:

[
4.3 \times 10^{-10} = \frac{x^2}{0.10 - x}
]

Approximate \(0.10 - x \approx 0.10\):

[
x^2 \approx 4.3 \times 10^{-11}
]
[
x \approx 6.56 \times 10^{-6}\,\text{M} = [\text{OH}^-]
]

Then:

[
pOH = -\log(6.56 \times 10^{-6}) \approx 5.18
]
[
pH = 14.00 - 5.18 = 8.82
]

This is a nice real example of determining pH of a weak base solution that is barely basic. Despite being 0.10 M, the pH is under 9 because the base is so weak.

Examples of determining pH of weak base solutions from conjugate acids

In real lab work, you often don’t get the base directly. Instead, you’re handed a salt of its conjugate acid and asked to find the pH. A classic case: ammonium chloride, NH₄Cl.

Ammonium chloride solution, 0.10 M

NH₄Cl is the salt of a weak base (NH₃) and a strong acid (HCl). In water, NH₄⁺ acts as a weak acid.

We can find the pH using \(K_a\) for NH₄⁺ or \(K_b\) for NH₃ plus \(K_w\).

Given:

• \(K_b(\text{NH}_3) = 1.8 \times 10^{-5}\)
• \(K_w = 1.0 \times 10^{-14}\)

Then:

[
K_a(\text{NH}_4^+) = \frac{K_w}{K_b} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} \approx 5.6 \times 10^{-10}
]

Now treat NH₄⁺ as a weak acid:

\[ \text{NH}_4^+ + \text{H}_2\text{O} \rightleftharpoons \text{NH}_3 + \text{H}_3\text{O}^+ \]

ICE table: \(0.10 - x, x, x\), and

[
5.6 \times 10^{-10} = \frac{x^2}{0.10 - x}
]

Approximate \(0.10 - x \approx 0.10\):

[
x^2 \approx 5.6 \times 10^{-11}
]
[
x \approx 7.5 \times 10^{-6}\,\text{M} = [\text{H}_3\text{O}^+]
]

[
pH = -\log(7.5 \times 10^{-6}) \approx 5.12
]

Why does this matter in a discussion of examples of determining pH of weak base solutions? Because in buffers, you often have both the weak base and its conjugate acid present, and you need to understand both sides of that equilibrium.

Buffer-style examples of determining pH of weak base solutions

Once you mix a weak base with its conjugate acid, you’re in buffer territory. Here, the Henderson–Hasselbalch equation for bases becomes incredibly handy.

For a base–conjugate acid pair:

[
pOH = pK_b + \log \left( \frac{[\text{BH}^+]}{[\text{B}]} \right)
]

and then \(pH = 14.00 - pOH\).

Example: NH₃/NH₄⁺ buffer

Suppose you prepare a solution with:

• 0.20 M NH₃
• 0.10 M NH₄Cl

Given \(K_b(\text{NH}_3) = 1.8 \times 10^{-5}\):

[
pK_b = -\log(1.8 \times 10^{-5}) \approx 4.74
]

Now:

[
pOH = 4.74 + \log \left( \frac{0.10}{0.20} \right) = 4.74 + \log(0.50)
]
[
\log(0.50) \approx -0.30
]
[
pOH \approx 4.74 - 0.30 = 4.44
]
[
pH = 14.00 - 4.44 = 9.56
]

This is one of the best examples of determining pH of weak base solutions when both base and conjugate acid are present. It mirrors real lab buffers used in biochemistry and analytical chemistry.

For context, many biological systems rely on weak acid–base pairs to maintain pH. While the classic biological buffer is the bicarbonate system (covered extensively by sources like NIH), the math you’re doing here with weak bases is the same style of reasoning.

Polyprotic and multi-site weak bases: another style of example

Some weak bases can accept more than one proton. A simple inorganic case is carbonate, \(\text{CO}_3^{2-}\), the conjugate base of bicarbonate.

In many general chemistry courses, you won’t be asked to go deep into all the steps, but you might see simplified examples of determining pH of weak base solutions that treat only the first protonation step as significant.

For carbonate:

\[ \text{CO}_3^{2-} + \text{H}_2\text{O} \rightleftharpoons \text{HCO}_3^- + \text{OH}^- \]

If you’re given \(K_b\) for this step (or \(K_a\) for \(\text{HCO}_3^-\) and asked to convert using \(K_w\)), you set up the same kind of ICE table and solve for \([\text{OH}^-]\). The structure of the calculation is no different from the earlier examples; the only twist is recognizing which \(K_b\) to use.

For more advanced work with polyprotic systems, university-level resources like LibreTexts Chemistry walk through full multi-equilibrium calculations.

Strategy: how to handle real examples of determining pH of weak base solutions

If you look back at all the examples of determining pH of weak base solutions above, a pattern emerges. You can treat almost every problem by following the same decision tree:

• Identify the base and write the equilibrium.
• Look up or compute \(K_b\) (or \(K_a\), then convert via \(K_w\)).
• Decide if you’re dealing with a simple base solution or a buffer-like mixture.
• For simple base solutions, use an ICE table and decide whether the \(x \ll C_0\) approximation is reasonable.
• For buffer solutions, use the Henderson–Hasselbalch equation for bases.
• For very dilute solutions, be wary of ignoring water autoionization.

This is exactly how professionals approach pH control in real systems, from industrial cleaners to pharmaceutical formulations. Regulatory and safety documents from agencies like the CDC and OSHA assume this kind of pH reasoning when they discuss handling of weakly basic solutions in the workplace.

By practicing multiple examples of determining pH of weak base solutions — ammonia at different concentrations, organic amines with different \(K_b\), buffer mixtures, and conjugate-acid salts — you build a flexible toolkit that applies across lab, industry, and biology.

FAQ: common questions with examples of weak base pH calculations

Q1: Can you give a quick example of determining pH of a 0.050 M weak base solution?
Suppose you have a weak base B with \(K_b = 1.0 \times 10^{-5}\) and initial concentration 0.050 M. Set up:

\[K_b = \frac{x^2}{0.050 - x} \approx \frac{x^2}{0.050}\]
\[x^2 \approx (1.0 \times 10^{-5})(0.050) = 5.0 \times 10^{-7}\]
\[x \approx 7.1 \times 10^{-4}\,\text{M} = [\text{OH}^-]\]
\[pOH \approx 3.15 \Rightarrow pH \approx 10.85\]

Q2: How do I know when the \(x \ll C_0\) approximation is valid for weak bases?
After solving for \(x\), compare \(x\) to the initial base concentration \(C_0\). If \(x/C_0\) is under about 5%, the approximation is usually acceptable for typical coursework. In the examples of determining pH of weak base solutions above, most approximations were under 2–3%.

Q3: Are there examples of weak base pH problems that absolutely require the quadratic formula?
Yes. If \(K_b\) is relatively large (the base is fairly strong as weak bases go) and the concentration is low enough that \(x\) is not negligible compared with \(C_0\), you should use the quadratic formula. A borderline example is the 0.20 M methylamine case; a more extreme case would be something like \(K_b = 1.0 \times 10^{-3}\) at \(C_0 = 0.010\,\text{M}\), where \(x\) becomes a substantial fraction of \(C_0\).

Q4: Where can I find more real examples of determining pH of weak base solutions?
University general chemistry sites and open textbooks are gold mines. Good starting points include LibreTexts Chemistry, NIST’s Chemistry WebBook, and many .edu general chemistry course pages that post problem sets with worked solutions.

Q5: Do temperature changes affect these examples of weak base pH calculations?
Yes. All the examples above assume 25 °C, where \(K_w = 1.0 \times 10^{-14}\) and \(pH + pOH = 14.00\). At higher or lower temperatures, \(K_w\) changes, so the neutral pH shifts and the relationship between pH and pOH adjusts. For most introductory problems, temperature is fixed at 25 °C, but in more advanced work (environmental chemistry, physiology, industrial processes), temperature dependence of \(K_w\) and \(K_b\) matters.