Calculate The Ph Of A 0.75 M Nh4Cl Solution

Acid-base chemistry calculator

Use this premium calculator to determine the pH of ammonium chloride solutions by modeling NH4+ as a weak acid. Adjust concentration, ammonia base constant, and solution method to see exact and approximate results with a live chart.

NH4Cl pH Calculator

For ammonium chloride, the acidic species is NH4+. The chloride ion is the conjugate base of a strong acid and does not hydrolyze meaningfully.

How to calculate the pH of a 0.75 m NH4Cl solution

To calculate the pH of a 0.75 m NH4Cl solution, you treat ammonium chloride as a salt that dissociates completely into NH4+ and Cl-. The chloride ion comes from hydrochloric acid, a strong acid, so Cl- is effectively neutral in water. The ammonium ion, however, is the conjugate acid of ammonia, a weak base. That means NH4+ can donate a proton to water and generate hydronium ions, making the solution acidic.

The key hydrolysis reaction is:

NH4+ + H2O ⇌ NH3 + H3O+

Because NH4+ is a weak acid, we usually calculate its acid dissociation constant from the known base dissociation constant of NH3. At 25°C, a common value for ammonia is Kb = 1.8 × 10^-5. Using the water ion product Kw = 1.0 × 10^-14, the acid constant of ammonium is:

Ka = Kw / Kb = (1.0 × 10^-14) / (1.8 × 10^-5) = 5.56 × 10^-10

Once you have Ka, the equilibrium expression for NH4+ is:

Ka = [H3O+][NH3] / [NH4+]

If the starting concentration of NH4+ is 0.75 and the amount dissociated is x, then at equilibrium:

• [NH4+] = 0.75 – x
• [NH3] = x
• [H3O+] = x

Substituting into the equilibrium expression gives:

Ka = x² / (0.75 – x)

Because Ka is very small, many students use the weak acid approximation and set 0.75 – x approximately equal to 0.75. Then:

x = √(Ka × C) = √(5.56 × 10^-10 × 0.75) ≈ 2.04 × 10^-5

This x value is the hydronium concentration, so:

pH = -log(2.04 × 10^-5) ≈ 4.69

Final answer: the pH of a 0.75 m NH4Cl solution at 25°C is approximately 4.69, assuming ideal behavior and using Kb(NH3) = 1.8 × 10^-5.

Why NH4Cl gives an acidic solution

Ammonium chloride is formed from a weak base, NH3, and a strong acid, HCl. Salts of weak bases and strong acids almost always yield acidic aqueous solutions. That happens because the cation retains measurable acidity. In contrast, the anion from a strong acid is too weak a base to significantly consume protons.

Ion behavior in water

• NH4+ acts as a weak acid and donates protons.
• Cl- is spectator-like in acid-base equilibrium.
• The result is an increase in hydronium concentration and a pH below 7.

This is a standard example in general chemistry because it demonstrates how the parent acid and parent base determine whether a salt solution is acidic, basic, or neutral. If you remember this pattern, many salt hydrolysis questions become much easier.

Step-by-step method for students

1. Write the dissociation of the salt: NH4Cl → NH4+ + Cl-.
2. Identify the ion that reacts with water: NH4+.
3. Write the hydrolysis equation: NH4+ + H2O ⇌ NH3 + H3O+.
4. Find Ka from Ka = Kw / Kb.
5. Set up an ICE table using initial NH4+ concentration of 0.75.
6. Solve for x using the exact quadratic method or the weak acid approximation.
7. Use pH = -log[H3O+].
8. Check whether the approximation is valid by comparing x with the initial concentration.

Approximation check

For the approximation to be valid, x should usually be less than 5% of the initial concentration. Here, x is about 2.04 × 10^-5, while the initial concentration is 0.75. The fraction dissociated is therefore:

(2.04 × 10^-5 / 0.75) × 100 ≈ 0.0027%

That is far below 5%, so the approximation is excellent.

Exact quadratic calculation

The exact treatment avoids approximation and solves:

x² + Ka x – KaC = 0

For C = 0.75 and Ka = 5.56 × 10^-10, the physically meaningful root is:

x = [-Ka + √(Ka² + 4KaC)] / 2

This yields nearly the same answer as the shortcut, which is why instructors often allow the square-root method for weak acid salts at moderate concentration. The calculator above supports both methods so you can compare them directly.

Reference constants and source-quality data

Acid-base calculations depend strongly on equilibrium constants and temperature. The values below are representative 25°C textbook constants commonly used in college chemistry.

Quantity	Typical value at 25°C	Why it matters
Kw for water	1.0 × 10^-14	Used to convert between Ka and Kb for conjugate pairs.
Kb of NH3	1.8 × 10^-5	Determines the conjugate acid strength of NH4+.
Ka of NH4+	5.56 × 10^-10	Controls how much hydronium is produced from NH4+ hydrolysis.
pKb of NH3	4.74	Alternative logarithmic form commonly used in hand calculations.
pKa of NH4+	9.25	Shows NH4+ is a weak acid, not a strong one.

How concentration affects NH4Cl solution pH

As NH4Cl concentration increases, the hydronium concentration generated by ammonium hydrolysis also rises, but not linearly. For weak acids, hydronium often scales approximately with the square root of concentration. This means increasing concentration by a factor of 10 lowers the pH, but not by a full unit in many cases.

NH4Cl concentration	Approximate [H3O+]	Approximate pH	Interpretation
0.010 M	2.36 × 10^-6 M	5.63	Mildly acidic, weak hydrolysis effect.
0.050 M	5.27 × 10^-6 M	5.28	More acidic, common lab concentration range.
0.10 M	7.46 × 10^-6 M	5.13	Textbook weak-acid salt example.
0.50 M	1.67 × 10^-5 M	4.78	Clearly acidic, approximation still very good.
0.75 M	2.04 × 10^-5 M	4.69	Your target problem.
1.00 M	2.36 × 10^-5 M	4.63	Higher ionic strength may slightly shift ideal behavior.

Molality versus molarity in this problem

The prompt specifies 0.75 m, where lowercase m normally means molality, not molarity. Strictly speaking, molality is moles of solute per kilogram of solvent, while molarity is moles of solute per liter of solution. For many classroom acid-base exercises, a 0.75 m aqueous solution is treated approximately like a 0.75 M solution unless density or activity corrections are specifically required.

In advanced analytical chemistry or physical chemistry, concentrated electrolyte solutions may require activity coefficients, ionic strength corrections, and more careful treatment of density. However, in standard general chemistry contexts, the expected answer is still around pH 4.69. If your instructor emphasizes thermodynamic activities rather than concentrations, the exact real-world pH can differ slightly.

Common mistakes to avoid

• Using HCl chemistry instead of NH4+ chemistry. NH4Cl is not a strong acid itself in water; it is a salt that produces an acidic cation.
• Forgetting to convert from Kb to Ka. You usually know Kb for NH3, not Ka for NH4+.
• Letting Cl- react in the equilibrium. Chloride is the conjugate base of a strong acid and is negligibly basic.
• Using pH = -log(0.75). That would incorrectly treat NH4Cl as fully dissociating into H3O+, which it does not.
• Ignoring temperature. Kw changes with temperature, so Ka derived from Kw/Kb also changes.

When to use exact vs approximate methods

Use the approximation when:

• The acid or base is weak.
• The concentration is much larger than the dissociated amount.
• The 5% rule is comfortably satisfied.

Use the exact quadratic when:

• Your instructor requires rigorous equilibrium work.
• The equilibrium constant is not extremely small.
• The solution is very dilute.
• You want to verify that your shortcut is valid.

For 0.75 m NH4Cl, both methods agree to practical reporting precision, which is why many solutions manuals present the square-root estimate.

Authoritative chemistry references

If you want to verify the chemistry principles, acid-base constants, and water equilibrium relationships, these authoritative educational and government sources are useful:

• LibreTexts Chemistry for broad educational explanations of salt hydrolysis and weak acid equilibria.
• National Institute of Standards and Technology (NIST) for standards-related scientific resources and reference-quality chemistry data context.
• University of California, Berkeley Chemistry for academic chemistry teaching resources and acid-base concepts.

Practical interpretation of the result

A pH of about 4.69 means the solution is acidic but far from strongly acidic. In practical terms, ammonium chloride solutions are commonly used in laboratory demonstrations, buffer preparation, fertilizer chemistry discussions, and biological or environmental contexts where ammonium speciation matters. The pH value tells you that a significant excess of NH4+ remains undissociated relative to NH3, which fits the weak-acid behavior of ammonium.

This also explains why NH4Cl is often paired with NH3 in buffer systems. Adding ammonia shifts the NH4+/NH3 ratio and allows controlled pH behavior near the pKa of ammonium, around 9.25. By itself, however, NH4Cl in water gives an acidic solution because no appreciable basic partner is present to consume the protons produced by hydrolysis.

Bottom line

To calculate the pH of a 0.75 m NH4Cl solution, identify NH4+ as the weak acid, calculate its Ka from the Kb of NH3, solve for hydronium concentration, and convert to pH. Using standard 25°C constants, the expected result is pH ≈ 4.69. The calculator on this page automates that full process and visualizes how the pH changes if you alter the concentration or equilibrium constants.

Educational note: this calculator uses concentration-based equilibrium expressions suitable for typical textbook and classroom problems. Highly concentrated or non-ideal solutions may require activity corrections for maximum rigor.