Calculate the pH of a 0.10 M Solution of Hydrazine
Use this interactive chemistry calculator to determine pH, pOH, hydroxide concentration, hydrazinium ion concentration, and percent ionization for aqueous hydrazine, N2H4. The tool applies weak-base equilibrium using the accepted base dissociation constant at 25 degrees Celsius and visualizes the result with a live chart.
Default calculation assumes hydrazine behaves as a weak base: N2H4 + H2O ⇌ N2H5+ + OH–. For a 0.10 M solution with Kb = 1.3 × 10-6, the expected pH is about 10.56 at 25 degrees C.
Expert Guide: How to Calculate the pH of a 0.10 M Solution of Hydrazine
Hydrazine, N2H4, is a classic example of a weak Brønsted base in aqueous chemistry. When you are asked to calculate the pH of a 0.10 M solution of hydrazine, the key idea is that hydrazine does not fully ionize like a strong base such as sodium hydroxide. Instead, only a small fraction of dissolved hydrazine molecules react with water to generate hydroxide ions. That limited ionization means the calculation must be done with equilibrium methods, not with the simple direct concentration approach used for strong bases.
This is why hydrazine problems appear so often in general chemistry and analytical chemistry courses. They test whether you can translate a chemical equation into an equilibrium expression, decide whether an approximation is valid, and convert the hydroxide concentration into pOH and then pH. The chemistry is practical as well. Hydrazine and hydrazine derivatives have been used in propellants, industrial synthesis, oxygen scavenging systems, and specialty chemical applications, so understanding its behavior in water is more than a textbook exercise.
Step 1: Write the Base Reaction
The first and most important step is writing the equilibrium for hydrazine acting as a base in water:
In this reaction, hydrazine accepts a proton from water to form the hydrazinium ion, N2H5+, and hydroxide ion, OH–. Because hydroxide is produced, the solution is basic, so the final pH must be greater than 7 at 25 degrees C.
Step 2: Use the Kb Expression
For a weak base, the equilibrium constant is the base dissociation constant, Kb. For hydrazine at 25 degrees C, a commonly cited value is approximately 1.3 × 10-6. The equilibrium expression is:
Notice that liquid water is omitted from the expression because it is the solvent and its activity is treated as constant. This is standard equilibrium practice for reactions in dilute aqueous solutions.
Step 3: Set Up an ICE Table
ICE stands for Initial, Change, and Equilibrium. If the initial concentration of hydrazine is 0.10 M and there is effectively no hydrazinium or hydroxide from hydrazine present initially, then the table is:
- Initial: [N2H4] = 0.10, [N2H5+] = 0, [OH–] = 0
- Change: -x, +x, +x
- Equilibrium: 0.10 – x, x, x
Substituting these terms into the Kb expression gives:
Step 4: Solve for x, the Hydroxide Concentration
Since hydrazine is a weak base and Kb is small, x will be much smaller than 0.10. That allows the common weak-base approximation:
Then the expression simplifies to:
That means the hydroxide concentration is about 3.61 × 10-4 M. Because the hydrazinium ion is produced in the same amount, [N2H5+] is also about 3.61 × 10-4 M.
If you prefer the exact solution, solve the quadratic equation x2 + Kb x – Kb C = 0. Doing that yields essentially the same value for x in this case because the approximation is excellent.
Step 5: Convert Hydroxide Concentration to pOH and pH
Now compute pOH:
At 25 degrees C, pH + pOH = 14.00, so:
Therefore, the pH of a 0.10 M hydrazine solution is approximately 10.56. That is the standard textbook answer when Kb = 1.3 × 10-6 is used.
Why the Approximation Works
Students are often told to check whether x is less than 5 percent of the initial concentration. Here, x = 3.61 × 10-4 and the initial concentration is 0.10 M. The percent ionization is:
Since 0.36 percent is far below 5 percent, the approximation is valid. This means replacing 0.10 – x with 0.10 introduces only a very small error.
Common Mistakes in Hydrazine pH Problems
- Treating hydrazine as a strong base. If you assume [OH–] = 0.10 M directly, you would get pOH = 1 and pH = 13, which is dramatically wrong.
- Using Ka instead of Kb. Hydrazine is acting as a base here, so the relevant constant is Kb unless you are specifically converting through the conjugate acid.
- Forgetting the stoichiometry. The reaction produces one mole of OH– per mole of hydrazinium ion formed, so both equilibrium concentrations are x.
- Neglecting the pOH step. Since hydrazine generates OH–, you typically find pOH first and then convert to pH.
- Using inconsistent Kb values. Different references may report values that vary slightly due to temperature or data source conventions. Small differences in Kb change the final pH slightly.
Worked Summary for the 0.10 M Case
- Initial hydrazine concentration, C = 0.10 M
- Hydrazine base constant, Kb = 1.3 × 10-6
- Set up equilibrium: Kb = x2 / (0.10 – x)
- Approximate: x = √(Kb × C) = √(1.3 × 10-7) = 3.61 × 10-4 M
- [OH–] = 3.61 × 10-4 M
- pOH = 3.44
- pH = 10.56
Comparison Table: Hydrazine vs Strong and Weak Bases
The table below helps place hydrazine in context. It shows how a 0.10 M solution compares with other familiar bases. Strong bases fully dissociate, while weak bases require equilibrium calculations.
| Base | Type | Characteristic Constant | Approximate pH at 0.10 M | Notes |
|---|---|---|---|---|
| Sodium hydroxide, NaOH | Strong base | Essentially complete dissociation | 13.00 | Directly gives [OH–] = 0.10 M |
| Ammonia, NH3 | Weak base | Kb ≈ 1.8 × 10-5 | 11.13 | More basic than hydrazine at the same concentration |
| Hydrazine, N2H4 | Weak base | Kb ≈ 1.3 × 10-6 | 10.56 | Produces much less OH– than a strong base |
| Aniline, C6H5NH2 | Weak base | Kb ≈ 4.3 × 10-10 | 8.82 | Far weaker due to resonance effects |
How Sensitive Is the pH to Kb?
Because hydrazine is a weak base, the pH depends on the square root of Kb times concentration under the usual approximation. That means doubling Kb does not double the hydroxide concentration; it only increases it by a factor of the square root of 2. This is useful when comparing data from different handbooks or temperatures.
| Kb Assumed | [OH–] in 0.10 M Solution | pOH | pH at 25 degrees C |
|---|---|---|---|
| 1.0 × 10-6 | 3.16 × 10-4 M | 3.500 | 10.500 |
| 1.3 × 10-6 | 3.61 × 10-4 M | 3.443 | 10.557 |
| 1.6 × 10-6 | 4.00 × 10-4 M | 3.398 | 10.602 |
Understanding the Chemistry Behind the Answer
Why is hydrazine less basic than sodium hydroxide but still clearly basic in water? The answer lies in the difference between dissociation and proton-transfer equilibrium. Sodium hydroxide is ionic and dissociates almost completely, so the hydroxide concentration is essentially equal to the dissolved base concentration. Hydrazine is molecular. It can accept a proton from water, but that reaction is only modestly favorable, so the equilibrium lies mostly to the reactant side. The result is that only a small percentage of hydrazine molecules become protonated, and only a small amount of hydroxide is produced.
Hydrazine also has two nitrogen atoms, and discussions of its structure sometimes lead students to assume it should be much stronger than ammonia. In practice, its measured Kb shows it is still a weak base. The actual basicity reflects electron distribution, solvation, and the stability of the conjugate acid in water, not just a simple count of lone pairs.
What If the Problem Says 0.10 m Instead of 0.10 M?
In many introductory problems, uppercase M indicates molarity and lowercase m indicates molality. Strictly speaking, these are not the same. Molarity is moles of solute per liter of solution, while molality is moles of solute per kilogram of solvent. However, for a dilute aqueous solution such as 0.10 units in water, the numerical difference between 0.10 M and 0.10 m is usually small enough that classroom equilibrium problems often treat them similarly unless density data are explicitly provided. This calculator includes a unit selector and notes that a molal input is approximated as dilute aqueous behavior.
Authority Sources for Further Study
For reliable background on acid-base chemistry, water quality pH fundamentals, and chemical safety context, review these authoritative resources:
- U.S. Environmental Protection Agency: Measurement of pH
- National Institute of Standards and Technology: NIST Chemistry WebBook
- LibreTexts Chemistry, hosted by higher education institutions
Final Answer
If you are solving the standard textbook problem, the pH of a 0.10 M solution of hydrazine is approximately 10.56, assuming Kb = 1.3 × 10-6 and pKw = 14.00 at 25 degrees C. The corresponding hydroxide concentration is about 3.61 × 10-4 M, the pOH is about 3.44, and the percent ionization is only about 0.36 percent. That low percent ionization confirms that hydrazine is a weak base and that the usual approximation is valid.
Use the calculator above if you want to explore how the answer changes when concentration, Kb, or pKw are adjusted. That is a powerful way to build intuition for weak-base equilibria and to see why pH depends on both intrinsic basicity and starting concentration.