Calculate the pH of 0.10 M HONH2
This interactive calculator solves the weak base equilibrium for hydroxylamine, HONH2, using either the exact quadratic method or the standard weak base approximation. Enter your concentration and Kb value, then generate a chart and step by step results instantly.
Weak Base pH Calculator
Default values are set to the common textbook problem: find the pH of a 0.10 M hydroxylamine solution at 25 degrees C.
Visual Summary
The chart compares exact pH, approximate pH, pOH, and the fraction of hydroxylamine ionized.
How to calculate the pH of 0.10 M HONH2
If you are asked to calculate the pH of 0.10 M HONH2, you are working with a classic weak base equilibrium problem. HONH2 is hydroxylamine, a nitrogen containing base that reacts with water to produce its conjugate acid and hydroxide ions. Because it is a weak base, it does not fully ionize in water. That means you cannot simply assume the hydroxide concentration equals 0.10 M. Instead, you must use an equilibrium expression based on the base dissociation constant, Kb.
The key reaction is:
For this reaction, the equilibrium constant expression is:
Most textbook and general chemistry examples use a Kb for hydroxylamine near 1.1 × 10-8 at 25 degrees C. With an initial concentration of 0.10 M, the solution is basic, but only mildly so because the Kb value is much smaller than 1. The correct pH comes out near 9.52, depending on the exact Kb and temperature assumptions used by the textbook or instructor.
Step 1: Set up the ICE table
The standard approach is to create an ICE table, which tracks Initial, Change, and Equilibrium concentrations.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HONH2 | 0.10 | -x | 0.10 – x |
| HONH3+ | 0 | +x | x |
| OH– | 0 | +x | x |
Substitute the equilibrium values into the Kb expression:
Because the Kb is very small relative to the initial concentration, x will be very small. In many classes, you can first test the approximation that 0.10 – x is essentially 0.10.
Step 2: Use the weak base approximation
When x is small, the expression simplifies to:
Now solve for x:
- x2 = (1.1 × 10-8)(0.10) = 1.1 × 10-9
- x = √(1.1 × 10-9) ≈ 3.32 × 10-5 M
Since x represents the hydroxide concentration at equilibrium:
Now calculate pOH:
Finally, convert pOH to pH at 25 degrees C:
That is the standard answer: the pH of 0.10 M HONH2 is about 9.52.
Step 3: Check whether the approximation is valid
In weak acid and weak base calculations, the 5 percent rule is used to test whether the small x assumption is acceptable.
Compute the percent ionization:
Because 0.033 percent is far below 5 percent, the approximation is excellent. That means the simplified method and the exact quadratic method give nearly identical answers.
Exact quadratic method
If your instructor requires exact work, solve the full equation:
Rearrange into standard quadratic form:
Using C = 0.10 and Kb = 1.1 × 10-8:
The positive root produces a hydroxide concentration that is essentially the same as the approximation. The resulting pH still rounds to about 9.52.
Why HONH2 is only mildly basic
Students sometimes expect any nitrogen base to create a strongly basic solution. That is not always true. The strength of a base depends on how effectively it accepts a proton from water and how stable the conjugate acid becomes. Hydroxylamine is weaker than ammonia by several orders of magnitude. As a result, even a 0.10 M solution produces only a modest hydroxide concentration.
The comparison below shows why the pH is not extremely high.
| Weak base | Approximate Kb at 25 degrees C | Relative basicity vs HONH2 | Notes |
|---|---|---|---|
| Hydroxylamine, HONH2 | 1.1 × 10-8 | 1× | Reference value used in this calculator |
| Pyridine, C5H5N | 1.7 × 10-9 | 0.15× | Weaker base than hydroxylamine |
| Ammonia, NH3 | 1.8 × 10-5 | About 1636× | Much stronger common weak base |
| Methylamine, CH3NH2 | 4.4 × 10-4 | About 40000× | Far stronger weak base in water |
| Aniline, C6H5NH2 | 4.3 × 10-10 | 0.039× | Very weak aromatic amine base |
These values help explain why a 0.10 M hydroxylamine solution is basic, but nowhere close to the pH of a strong base. For example, a 0.10 M NaOH solution would have [OH–] = 0.10 M directly, giving pOH = 1 and pH = 13 at 25 degrees C. In contrast, hydroxylamine only generates hydroxide on the order of 10-5 M.
Calculated pH values for HONH2 at several concentrations
One of the best ways to understand weak base behavior is to compare concentration changes. The following table uses Kb = 1.1 × 10-8 at 25 degrees C and applies the weak base model to several initial concentrations of hydroxylamine.
| Initial HONH2 concentration (M) | Approximate [OH–] (M) | pOH | pH | Percent ionization |
|---|---|---|---|---|
| 1.0 | 1.05 × 10-4 | 3.98 | 10.02 | 0.010 percent |
| 0.10 | 3.32 × 10-5 | 4.48 | 9.52 | 0.033 percent |
| 0.010 | 1.05 × 10-5 | 4.98 | 9.02 | 0.105 percent |
| 0.0010 | 3.32 × 10-6 | 5.48 | 8.52 | 0.332 percent |
Notice two important trends. First, pH increases as concentration increases. Second, percent ionization becomes larger as the base becomes more dilute. That second trend is typical of weak electrolytes.
Most common mistakes when solving this problem
- Treating HONH2 as a strong base. It is weak, so [OH–] is not 0.10 M.
- Using Ka instead of Kb. Hydroxylamine is a base in this problem, so the relevant equilibrium constant is Kb.
- Forgetting to convert pOH to pH. After finding [OH–], you must calculate pOH first, then pH.
- Using the wrong logarithm. Chemistry pH calculations use base 10 logarithms.
- Ignoring significant figures. If the concentration is given as 0.10 M, the final pH often appears as 9.52 or 9.53 depending on the Kb value used.
Shortcut method for exams
If you are under time pressure, memorize this weak base shortcut:
For this problem:
- Multiply Kb and concentration: 1.1 × 10-8 × 0.10 = 1.1 × 10-9
- Take the square root: √(1.1 × 10-9) = 3.32 × 10-5
- Find pOH = 4.48
- Find pH = 9.52
This approach is fast, accurate, and fully justified because the percent ionization is tiny.
How temperature and data source can change the answer slightly
In some references, you may see slightly different Kb values for hydroxylamine or slightly different pKw assumptions at temperatures other than 25 degrees C. Those changes can shift the final pH in the second decimal place. That is normal. In chemistry, equilibrium constants are experimentally determined and often reported with small differences across sources or conditions. For most general chemistry courses, using Kb = 1.1 × 10-8 and pKw = 14.00 at 25 degrees C is perfectly appropriate.
Authoritative chemistry references
For broader background on pH, equilibria, and acid base chemistry, review these reputable sources:
U.S. Environmental Protection Agency: What is pH?
University of Wisconsin chemistry acid base equilibrium tutorial
National Institute of Standards and Technology
Final answer
To calculate the pH of 0.10 M HONH2, write the weak base equilibrium, apply the Kb expression, solve for the hydroxide concentration, and convert through pOH to pH. Using a typical value of Kb = 1.1 × 10-8 at 25 degrees C, the solution gives:
That is the result your calculator should produce for the standard problem. If you want to verify the work, compare the exact quadratic answer with the approximation. Both should agree to normal rounding precision, which confirms that the small x assumption is valid for this concentration.