Calculate The Ph Of A 0.0750 M Solution Of Ammonia

Use this premium weak base calculator to find pH, pOH, hydroxide concentration, and percent ionization for aqueous ammonia. The default setup solves the exact equilibrium for a 0.0750 M NH₃ solution at 25 degrees Celsius using K_b = 1.8 × 10^-5.

Ammonia pH Calculator

Equilibrium Model

Reaction: NH₃ + H₂O ⇌ NH₄⁺ + OH^–

K_b expression: K_b = [NH₄⁺][OH^–] / [NH₃]

• Initial NH₃ concentration = C
• Change = x for NH₄⁺ and OH^–
• Equilibrium concentrations: [NH₄⁺] = x, [OH^–] = x, [NH₃] = C – x

Exact equation: x² / (C – x) = K_b

This rearranges to x² + K_bx – K_bC = 0, where x = [OH^–].

Expert Guide: How to Calculate the pH of a 0.0750 M Solution of Ammonia

Calculating the pH of a 0.0750 M solution of ammonia is a classic weak base equilibrium problem in general chemistry. It tests your understanding of K_b, ICE tables, pOH, and the relationship between pH and pOH. Unlike a strong base such as sodium hydroxide, ammonia does not fully dissociate in water. Instead, only a small fraction of NH₃ molecules accept a proton from water to produce ammonium ions and hydroxide ions. That partial ionization is exactly why the equilibrium approach matters.

For a solution containing ammonia, the relevant equilibrium is:

NH₃ + H₂O ⇌ NH₄⁺ + OH^–

Because ammonia is a weak base, you do not simply set the hydroxide concentration equal to the starting concentration. Instead, you use the base dissociation constant, K_b, to determine how much OH^– forms at equilibrium. At 25 degrees Celsius, a common textbook K_b value for ammonia is 1.8 × 10^-5. With an initial concentration of 0.0750 M, the final pH is basic, but not nearly as high as it would be for a strong base at the same concentration.

Step 1: Write the balanced weak base equilibrium

The first step in any acid-base equilibrium problem is to identify the chemical reaction in water. For ammonia:

• NH₃ acts as a Brønsted-Lowry base.
• Water acts as the acid and donates a proton.
• The products are NH₄⁺ and OH^–.

This reaction tells us immediately that the pH will be above 7 because hydroxide ions are produced. However, because NH₃ is weak, the amount of OH^– produced must be calculated from equilibrium data instead of being assumed complete.

Step 2: Set up the ICE table

An ICE table is the standard tool for organizing weak acid and weak base problems. Let the initial ammonia concentration be 0.0750 M and let x represent the amount that reacts.

Species	Initial (M)	Change (M)	Equilibrium (M)
NH3	0.0750	-x	0.0750 – x
NH4^+	0	+x	x
OH^–	0	+x	x

From this setup, the equilibrium expression becomes:

K_b = x² / (0.0750 – x)

Step 3: Insert the K_b value for ammonia

Using K_b = 1.8 × 10^-5, substitute into the expression:

1.8 × 10^-5 = x² / (0.0750 – x)

At this stage, many instructors allow the weak base approximation because x is typically small relative to the initial concentration. If x is much smaller than 0.0750, then:

0.0750 – x ≈ 0.0750

This gives:

x² = (1.8 × 10^-5)(0.0750)

x² = 1.35 × 10^-6

x = 0.001162 M

Since x represents [OH^–], you can now compute pOH:

pOH = -log(0.001162) = 2.93

pH = 14.00 – 2.93 = 11.07

Answer: The pH of a 0.0750 M ammonia solution is approximately 11.07 at 25 degrees Celsius when K_b = 1.8 × 10^-5.

Step 4: Check whether the approximation is valid

The 5 percent rule is often used to confirm that the weak base approximation is acceptable. Compare x to the initial concentration:

(0.001162 / 0.0750) × 100 = 1.55%

Because 1.55 percent is less than 5 percent, the approximation is valid. That means the shortcut method gives a reliable result for this problem.

Still, the exact quadratic approach is the gold standard and is what this calculator can solve automatically. Starting from:

x² / (C – x) = K_b

Rearrange to:

x² + K_bx – K_bC = 0

For C = 0.0750 and K_b = 1.8 × 10^-5, solving the quadratic gives essentially the same x value, so the pH remains about 11.07.

Why ammonia is treated as a weak base

Students often ask why ammonia, which clearly creates a basic solution, is not classified as a strong base. The reason is that strength in acid-base chemistry refers to extent of ionization, not whether the pH is simply above 7. Strong bases such as NaOH or KOH dissociate almost completely in water, while ammonia only reacts partially with water. Most of the dissolved NH₃ remains as NH₃, and only a small portion becomes NH₄⁺ and OH^–.

This distinction explains why a 0.0750 M ammonia solution has a pH around 11.07, while a 0.0750 M sodium hydroxide solution would have a much higher pH. In strong base calculations, [OH^–] is usually equal to the analytical concentration. In weak base calculations, [OH^–] is generated according to K_b.

Comparison table: weak base versus strong base at the same formal concentration

Solution	Formal concentration (M)	Assumed [OH^–] at equilibrium	pOH	pH
NH3 (weak base, Kb = 1.8 × 10^-5)	0.0750	0.00116 M	2.93	11.07
NaOH (strong base)	0.0750	0.0750 M	1.12	12.88

This is a powerful comparison because it shows that equal molar concentration does not imply equal pH. Base strength matters just as much as concentration.

Percent ionization of 0.0750 M ammonia

Another useful quantity is the percent ionization, which measures the fraction of NH₃ that reacts with water. The expression is:

Percent ionization = (x / initial concentration) × 100

Substitute the values:

(0.001162 / 0.0750) × 100 = 1.55%

That means more than 98 percent of the ammonia remains un-ionized under these conditions. This is exactly the pattern expected for a weak base with a small K_b.

How pH changes with ammonia concentration

The pH of ammonia solutions rises as concentration increases, but not in a perfectly linear way. Because ammonia is a weak base, the relationship follows equilibrium behavior. Doubling or tripling the concentration does not double or triple the hydroxide concentration. Instead, [OH^–] depends approximately on the square root of K_bC when the weak base approximation is valid.

Initial NH3 concentration (M)	Approximate [OH^–] (M)	Approximate pOH	Approximate pH
0.0100	4.24 × 10^-4	3.37	10.63
0.0500	9.49 × 10^-4	3.02	10.98
0.0750	1.16 × 10^-3	2.93	11.07
0.1000	1.34 × 10^-3	2.87	11.13
0.5000	3.00 × 10^-3	2.52	11.48

Common mistakes when solving this problem

1. Treating ammonia as a strong base. This leads to a huge overestimate of [OH^–] and pH.
2. Using K_a instead of K_b. Ammonia is a base, so K_b is the correct equilibrium constant unless you convert using K_w.
3. Forgetting to convert pOH to pH. Weak base calculations often give [OH^–] first, so pOH comes before pH.
4. Skipping the approximation check. The 5 percent rule helps confirm whether the square root shortcut is justified.
5. Rounding too early. Carry enough significant figures through the intermediate steps to preserve a reliable final pH.

When should you use the quadratic formula?

The approximation x = √(K_bC) works well when K_b is small and the concentration is not too dilute. However, if the concentration is very low or the equilibrium constant is larger, x may not be negligible relative to C. In those cases, the exact quadratic solution is the better approach. Modern calculators and chemistry software can solve it instantly, and this page does that for you.

Interpretation of the final answer

A pH of about 11.07 means the solution is clearly basic, but still far weaker than a similarly concentrated strong base. In practical terms, aqueous ammonia is basic enough to alter indicator colors, neutralize acids, and participate in buffer systems with ammonium salts. The moderate pH also explains why ammonia is widely discussed in environmental chemistry, analytical chemistry, and industrial process chemistry.

Because pH is logarithmic, even modest differences in pH correspond to meaningful differences in hydroxide ion concentration. That is why careful equilibrium calculations matter. Getting the pH right is not just a bookkeeping exercise. It directly affects reaction conditions, solubility, speciation, and safety decisions.

Authoritative references for ammonia and acid-base equilibrium

• NIST Chemistry WebBook: Ammonia data
• U.S. EPA: Ammonia information and environmental context
• University of Wisconsin chemistry resource on acid-base equilibria

Final summary

To calculate the pH of a 0.0750 M ammonia solution, start with the weak base equilibrium, build an ICE table, apply the ammonia K_b, solve for hydroxide concentration, convert to pOH, and finally convert to pH. Using K_b = 1.8 × 10^-5, the solution gives [OH^–] ≈ 1.16 × 10^-3 M, pOH ≈ 2.93, and pH ≈ 11.07. The percent ionization is about 1.55 percent, confirming that ammonia behaves as a weak base under these conditions.

Note: pH values depend on temperature and the chosen thermodynamic constants. This calculator uses the standard educational assumption of 25 degrees Celsius and a commonly cited K_b value for NH₃.