Calculate the pH of a 1.07 m Solution of NH4Cl
Use this interactive chemistry calculator to determine the pH of an ammonium chloride solution from molality and the base dissociation constant of ammonia. The tool uses the ammonium ion hydrolysis equilibrium and solves for hydronium concentration with the quadratic expression for higher accuracy.
Results
This default result corresponds to a 1.07 m NH4Cl solution at 25°C using Kb(NH3) = 1.8 × 10-5.
Expert Guide: How to Calculate the pH of a 1.07 m Solution of NH4Cl
Calculating the pH of a 1.07 m solution of ammonium chloride, NH4Cl, is a classic weak acid equilibrium problem. Even though NH4Cl is a salt, its aqueous solution is not neutral. The key reason is that the ammonium ion, NH4+, is the conjugate acid of the weak base ammonia, NH3. When NH4Cl dissolves in water, the chloride ion behaves as a spectator ion, while NH4+ donates protons to water to a small extent, creating hydronium ions and lowering the pH below 7.
If you are working through general chemistry, analytical chemistry, environmental chemistry, or chemical engineering problems, this type of question helps you connect acid-base theory, equilibrium constants, and logarithmic pH calculations. The result for a 1.07 m NH4Cl solution at 25°C is typically about pH 4.61 when you use the common literature value Kb for NH3 = 1.8 × 10-5 and convert to the acid constant of NH4+ with Ka = Kw/Kb.
Step 1: Recognize the Chemistry of NH4Cl in Water
Ammonium chloride is composed of NH4+ and Cl-. In water it dissociates essentially completely:
NH4Cl(aq) → NH4+(aq) + Cl-(aq)
The chloride ion comes from hydrochloric acid, a strong acid, so Cl- has negligible basicity in water. The ammonium ion, however, is a weak acid because it is the conjugate acid of ammonia:
NH4+(aq) + H2O(l) ⇌ NH3(aq) + H3O+(aq)
That equilibrium is what controls the pH. So the problem is not handled as a strong acid calculation. Instead, it is solved as a weak acid equilibrium using Ka for NH4+.
Step 2: Convert Kb of NH3 to Ka of NH4+
Most data tables provide the base dissociation constant of ammonia rather than the acid dissociation constant of ammonium. At 25°C, a common value is:
- Kb(NH3) = 1.8 × 10-5
- Kw = 1.0 × 10-14
For a conjugate acid-base pair, the relation is:
Ka × Kb = Kw
Therefore:
Ka(NH4+) = (1.0 × 10-14) / (1.8 × 10-5) = 5.56 × 10-10
This Ka value tells us that NH4+ is a weak acid, but not a strong one. Even in a relatively concentrated solution such as 1.07 m, only a tiny fraction of ammonium ions donate a proton.
Step 3: Set Up the Equilibrium Table
Assume the analytical concentration of NH4+ is about 1.07. Because the problem gives molality, there is a subtle thermodynamic distinction between molality and molarity, and very concentrated solutions can require activity corrections. In most introductory and many intermediate textbook settings, however, a 1.07 m salt solution is treated approximately as 1.07 M for the purpose of a pH equilibrium estimate unless density data are explicitly provided.
For the equilibrium:
NH4+ + H2O ⇌ NH3 + H3O+
- Initial: [NH4+] = 1.07, [NH3] = 0, [H3O+] ≈ 0
- Change: [NH4+] = -x, [NH3] = +x, [H3O+] = +x
- Equilibrium: [NH4+] = 1.07 – x, [NH3] = x, [H3O+] = x
Then write the acid dissociation expression:
Ka = ([NH3][H3O+]) / [NH4+] = x2 / (1.07 – x)
Step 4: Solve for x = [H3O+]
Insert the Ka value:
5.56 × 10-10 = x2 / (1.07 – x)
Because Ka is very small, you can often use the weak acid approximation and assume x is negligible compared with 1.07:
x2 / 1.07 = 5.56 × 10-10
x2 = 5.95 × 10-10
x = 2.44 × 10-5
So:
[H3O+] = 2.44 × 10-5 M
Now calculate pH:
pH = -log(2.44 × 10-5) = 4.61
If you solve the full quadratic instead of using the approximation, the result is essentially the same to the shown significant figures because x is tiny relative to 1.07.
Final Answer
The pH of a 1.07 m solution of NH4Cl is:
pH ≈ 4.61
Why the Solution Is Acidic, Not Neutral
Many students initially think that because NH4Cl is a salt, the solution should be neutral like sodium chloride. The important distinction is the acid-base strength of the parent acid and parent base. Sodium chloride comes from NaOH and HCl, both strong counterparts in water chemistry, so neither ion hydrolyzes appreciably. NH4Cl is different because NH4+ is the conjugate acid of a weak base, NH3. That makes NH4+ acidic in water.
| Salt | Cation Behavior | Anion Behavior | Expected pH Trend | Typical Example |
|---|---|---|---|---|
| NaCl | Na+ neutral spectator | Cl- neutral spectator | Near 7 | Strong base + strong acid |
| NH4Cl | NH4+ weak acid | Cl- neutral spectator | Below 7 | Weak base + strong acid |
| CH3COONa | Na+ neutral spectator | CH3COO- weak base | Above 7 | Strong base + weak acid |
| NH4CH3COO | NH4+ weak acid | CH3COO- weak base | Depends on Ka vs Kb | Weak base + weak acid |
Approximation Versus Exact Calculation
In weak acid and weak base problems, the common shortcut is to assume the equilibrium change x is small relative to the initial concentration C. This yields the very handy equation:
x ≈ √(KaC)
For NH4Cl at 1.07 concentration units, this approximation works extremely well because the acid dissociation constant is on the order of 10-10. The percentage ionization is only:
(2.44 × 10-5 / 1.07) × 100 ≈ 0.0023%
That is far below the typical 5% guideline used to justify the approximation. So whether you solve by approximation or by quadratic formula, the pH remains about 4.61.
Molality Versus Molarity in This Problem
The problem specifically states 1.07 m, where lowercase m denotes molality, defined as moles of solute per kilogram of solvent. Strictly speaking, equilibrium expressions in solution chemistry are written in terms of activities, and practical approximations often use molarity instead of molality. If a problem gives only molality and does not provide solution density or activity coefficients, most classroom solutions use the stated value as the working concentration for the weak acid calculation.
In more advanced physical chemistry or geochemistry work, a concentrated electrolyte like NH4Cl can show nonideal behavior. In that setting, the measured pH can differ from the simple ideal estimate because:
- Activity coefficients deviate from 1
- Ionic strength affects effective equilibrium constants
- The solution density may make molarity differ noticeably from molality
- Temperature changes alter both Kw and Kb
For textbook chemistry, though, pH ≈ 4.61 is the accepted result.
Useful Data for the NH4+/NH3 System
| Quantity | Typical Value at 25°C | Meaning | Role in pH Calculation |
|---|---|---|---|
| Kw | 1.0 × 10-14 | Ion product of water | Used to convert Kb to Ka |
| Kb of NH3 | 1.8 × 10-5 | Basicity of ammonia | Given or looked up |
| Ka of NH4+ | 5.56 × 10-10 | Acidity of ammonium ion | Directly governs [H3O+] |
| pKa of NH4+ | 9.25 | Negative log of Ka | Shows NH4+ is a weak acid |
| Solution concentration | 1.07 | Analytical concentration approximation | Initial NH4+ concentration |
| Calculated [H3O+] | 2.44 × 10-5 | Hydronium at equilibrium | Converted to pH |
Common Mistakes to Avoid
- Treating NH4Cl as a neutral salt. It is acidic because NH4+ hydrolyzes.
- Using Kb directly in the acid equilibrium expression. First convert Kb of NH3 to Ka of NH4+.
- Forgetting that Cl- is a spectator ion. Chloride does not materially raise the pH.
- Applying strong acid logic. NH4+ does not fully dissociate like HCl.
- Ignoring temperature dependence. If temperature changes, both Kw and Kb may change.
When Would the pH Change from 4.61?
The result changes if any of the following change:
- The concentration of NH4Cl
- The temperature, which changes Kw and often Kb
- The ionic strength and activity correction model
- The accepted tabulated Kb value of NH3 used by your class or text
- The solution density, if converting molality to molarity accurately
For example, a more dilute NH4Cl solution would have lower hydronium concentration and thus a higher pH. A more concentrated solution would generally have a lower pH, though nonideal effects may become more pronounced as concentration rises.
Authoritative References for Acid-Base Constants and pH Concepts
For deeper study, consult high-quality educational and government sources on acid-base equilibria, ammonia chemistry, and pH fundamentals:
- U.S. Environmental Protection Agency: pH overview and water chemistry context
- NIST Chemistry WebBook: reliable thermochemical and chemical property reference data
- University-level educational explanation of acid-base properties of salts
Summary
To calculate the pH of a 1.07 m solution of NH4Cl, identify NH4+ as a weak acid, convert the known ammonia base constant to the ammonium acid constant, and solve the weak acid equilibrium. Using Kb(NH3) = 1.8 × 10-5 and Kw = 1.0 × 10-14, you obtain Ka(NH4+) = 5.56 × 10-10. Substituting into the equilibrium expression gives [H3O+] = 2.44 × 10-5 and therefore pH = 4.61.
This is a great example of why salts can produce acidic or basic solutions depending on the nature of their ions. NH4Cl is not neutral in water. Because NH4+ is the conjugate acid of a weak base, the solution is acidic, and at 1.07 m the pH falls comfortably in the mildly acidic range.