Calculate the pH of the Following Solutions: 0.100 M HONH2
Use this interactive weak-base calculator to find the pH, pOH, hydroxide concentration, percent ionization, and equilibrium composition for hydroxylamine, HONH2. The default values are set for the classic chemistry problem: 0.100 M HONH2 at 25 degrees Celsius with Kb = 1.1 × 10^-8.
Results
Click Calculate pH to solve the 0.100 M HONH2 weak-base equilibrium problem.
Reaction modeled: HONH2 + H2O ⇌ HONH3+ + OH-. The calculator uses the exact equilibrium expression Kb = x² / (C – x), where x = [OH-].
How to Calculate the pH of 0.100 M HONH2
To calculate the pH of the following solution, 0.100 M HONH2, you need to recognize that hydroxylamine acts as a weak base in water. That means it does not completely dissociate the way a strong base such as sodium hydroxide does. Instead, it establishes an equilibrium with water:
HONH2 + H2O ⇌ HONH3+ + OH-
Because hydroxylamine generates hydroxide ions, the solution becomes basic, so the pH will be greater than 7. The challenge is that the amount of OH- produced is not equal to the full starting concentration. Instead, you must use the base dissociation constant, Kb, to determine the equilibrium concentration of hydroxide. For hydroxylamine at 25 degrees Celsius, a commonly used value is approximately 1.1 × 10^-8.
This is why many students find the problem slightly more involved than a simple pH or pOH calculation. You have to set up an ICE table, write the equilibrium expression, solve for x, and then convert that value into pOH and finally pH. Once you understand that process, you can solve not only 0.100 M HONH2 but nearly any weak base problem of the same type.
Step 1: Identify HONH2 as a Weak Base
HONH2, also written as NH2OH in many textbooks, is hydroxylamine. In aqueous solution it accepts a proton from water to form its conjugate acid, HONH3+, while generating hydroxide ions:
- Write the equilibrium reaction: HONH2 + H2O ⇌ HONH3+ + OH-
- Use the initial concentration: 0.100 M
- Apply the weak base constant: Kb = 1.1 × 10^-8
- Solve for the equilibrium hydroxide concentration
- Calculate pOH and then pH
Step 2: Set Up the ICE Table
An ICE table tracks Initial, Change, and Equilibrium concentrations. If we let x represent the amount of HONH2 that reacts, then:
- Initial [HONH2] = 0.100 M
- Initial [HONH3+] = 0
- Initial [OH-] = 0
At equilibrium:
- [HONH2] = 0.100 – x
- [HONH3+] = x
- [OH-] = x
The base dissociation expression is:
Kb = [HONH3+][OH-] / [HONH2]
Substituting the ICE table values gives:
1.1 × 10^-8 = x² / (0.100 – x)
Step 3: Solve for x
Since Kb is very small, many instructors allow the approximation that x is much smaller than 0.100. In that case:
1.1 × 10^-8 ≈ x² / 0.100
Multiply both sides by 0.100:
x² ≈ 1.1 × 10^-9
Take the square root:
x ≈ 3.32 × 10^-5 M
Since x equals [OH-], we now have:
[OH-] ≈ 3.32 × 10^-5 M
If you solve the equation exactly with the quadratic formula, the answer is essentially the same for practical classroom purposes. The exact solution is one reason this calculator is useful because it avoids rounding drift and verifies that the approximation is valid.
Step 4: Convert [OH-] to pOH and pH
Once [OH-] is known, calculate pOH:
pOH = -log(3.32 × 10^-5) ≈ 4.48
Then calculate pH:
pH = 14.00 – 4.48 = 9.52
Why the pH Is Not Extremely High
A common misunderstanding is to assume that a 0.100 M basic solution must have a pH near 13. That would be true for a strong base such as NaOH because nearly every formula unit contributes OH-. Hydroxylamine is different. Its Kb is small, so only a tiny fraction of HONH2 molecules react with water. That means the hydroxide concentration is much lower than 0.100 M, and the pH rises only to the moderate basic range around 9.5.
In fact, the percent ionization for this solution is only about:
(3.32 × 10^-5 / 0.100) × 100 ≈ 0.033%
That is an important check. Because the ionization is far below 5%, the small-x approximation is fully justified here.
Comparison Table: 0.100 M Weak Bases at 25 Degrees Celsius
The table below compares several familiar weak bases. The Kb values are representative textbook values at 25 degrees Celsius, and the pH values are approximate equilibrium pH values for 0.100 M solutions. This makes it easier to see where hydroxylamine fits on the weak-base strength scale.
| Base | Representative Kb | Approximate pH at 0.100 M | Interpretation |
|---|---|---|---|
| Hydroxylamine, HONH2 | 1.1 × 10^-8 | 9.52 | Weakly basic, limited ionization |
| Pyridine, C5H5N | 1.7 × 10^-9 | 9.12 | Weaker base than hydroxylamine |
| Ammonia, NH3 | 1.8 × 10^-5 | 11.13 | Much stronger weak base |
| Methylamine, CH3NH2 | 4.4 × 10^-4 | 11.82 | Significantly stronger weak base |
How Concentration Changes the pH of Hydroxylamine
Even when Kb stays constant, the pH of a weak base changes with concentration. A more concentrated hydroxylamine solution produces more OH- at equilibrium and therefore a higher pH. The increase is not linear because the chemistry follows an equilibrium expression rather than simple direct proportionality.
| Initial [HONH2] | Approximate [OH-] at Equilibrium | Approximate pOH | Approximate pH |
|---|---|---|---|
| 0.0010 M | 3.32 × 10^-6 M | 5.48 | 8.52 |
| 0.0100 M | 1.05 × 10^-5 M | 4.98 | 9.02 |
| 0.100 M | 3.32 × 10^-5 M | 4.48 | 9.52 |
| 1.000 M | 1.05 × 10^-4 M | 3.98 | 10.02 |
Most Common Mistakes in This Problem
- Using the acid formula instead of the base formula.
- Treating HONH2 as a strong base and assuming [OH-] = 0.100 M.
- Forgetting that the equilibrium expression for a weak base uses Kb, not Ka.
- Calculating pOH correctly but forgetting to convert to pH.
- Dropping the x term without checking whether the approximation is valid.
Exact vs Approximate Solution
In introductory chemistry, weak-base problems are often solved by approximation. For 0.100 M HONH2 this works beautifully because x is tiny compared with the starting concentration. Still, the exact method is more rigorous:
x = (-Kb + √(Kb² + 4KbC)) / 2
where C is the initial concentration. If you substitute Kb = 1.1 × 10^-8 and C = 0.100, you get x very close to 3.32 × 10^-5 M. The difference between the approximate and exact answers is negligible for most classroom work, but exact computation is ideal in a calculator because it remains accurate even when approximation conditions are borderline.
Why This Result Matters in Chemistry
Problems like this one train you to classify solutes correctly and apply equilibrium thinking. The pH of a weak base solution is not just a number to memorize. It tells you about proton affinity, conjugate acid formation, percent ionization, and how molecular structure affects solution behavior. Hydroxylamine is also relevant in inorganic, analytical, and synthetic chemistry contexts, so understanding its acid-base behavior is useful beyond the classroom.
Authoritative Resources for Further Study
If you want to verify equilibrium methods, weak-base theory, or hydroxylamine reference information, consult these authoritative educational and government sources:
- NIST Chemistry WebBook (.gov)
- Purdue University Chemistry Department (.edu)
- University of Wisconsin Chemistry resources (.edu)
Quick Final Summary
To calculate the pH of 0.100 M HONH2, treat hydroxylamine as a weak base, write the equilibrium reaction with water, use an ICE table, substitute into the Kb expression, solve for hydroxide concentration, and convert from pOH to pH. Using Kb = 1.1 × 10^-8, the equilibrium hydroxide concentration is about 3.32 × 10^-5 M, the pOH is about 4.48, and the pH is about 9.52.