Calculate Ph Of 0.2 M Aqueous Solution Of Sodium Butyrate

Use this interactive chemistry calculator to determine the pH, pOH, hydroxide concentration, percent hydrolysis, and related equilibrium values for sodium butyrate in water. The tool supports both the standard weak-base approximation and the exact quadratic method used in acid-base equilibrium analysis.

Sodium Butyrate pH Calculator

Core chemistry:
Butyrate ion acts as a weak base in water:
C₃H₇COO^– + H₂O ⇌ C₃H₇COOH + OH^–
K_b = K_w / K_a, then solve for [OH^–] and convert to pOH and pH.

Calculated Results

The chart compares pH across nearby sodium butyrate concentrations using the same pKa and temperature settings, helping you see how dilution affects weak-base hydrolysis.

Expert Guide: How to Calculate the pH of a 0.2 M Aqueous Solution of Sodium Butyrate

Sodium butyrate is the sodium salt of butyric acid, a weak carboxylic acid. Because it is a salt formed from a strong base and a weak acid, its aqueous solution is basic. That means if you dissolve sodium butyrate in water, the butyrate ion reacts with water to generate hydroxide ions, which raises the pH above 7. If your target is to calculate the pH of a 0.2 M aqueous solution of sodium butyrate, the correct chemistry framework is weak-base hydrolysis, not a strong base assumption.

The central idea is simple: sodium butyrate dissociates almost completely into sodium ions and butyrate ions in water. Sodium ions are spectators, while the butyrate ion acts as the conjugate base of butyric acid. Since conjugate bases of weak acids can accept protons from water, they produce OH^–. Once the hydroxide concentration is known, pOH and then pH can be calculated. For the commonly cited pKa of butyric acid near 4.82 at 25 C, the pH of a 0.2 M sodium butyrate solution comes out to approximately 9.06.

Why sodium butyrate makes water basic

In solution, sodium butyrate dissociates as:

C₃H₇COONa → Na⁺ + C₃H₇COO^–

The butyrate ion then hydrolyzes in water:

C₃H₇COO^– + H₂O ⇌ C₃H₇COOH + OH^–

This reaction produces hydroxide, so the solution is basic. Since the hydrolysis is weak, the OH^– concentration is much smaller than the original 0.2 M solute concentration. That is why equilibrium methods are needed.

Step-by-step calculation for 0.2 M sodium butyrate

1. Start with the acid dissociation constant information for butyric acid. A typical pKa value is 4.82.
2. Convert pKa to Ka using K_a = 10^-pKa.
3. Use the water relation K_b = K_w / K_a.
4. Set the initial butyrate concentration to 0.2 M.
5. Write the base hydrolysis equilibrium as K_b = x² / (C – x), where x = [OH^–].
6. Solve exactly with the quadratic equation or approximately with x ≈ √(K_bC) if x is small.
7. Calculate pOH = -log[OH^–].
8. At 25 C, calculate pH = 14.00 – pOH.

Worked example with real numbers

Let us carry out the full solution for the requested case.

• Given concentration, C = 0.2 M
• Given pKa of butyric acid, 4.82
• So K_a = 10^-4.82 ≈ 1.51 × 10^-5
• At 25 C, K_w = 1.00 × 10^-14
• Therefore K_b = 1.00 × 10^-14 / 1.51 × 10^-5 ≈ 6.61 × 10^-10

Now use the equilibrium relation:

K_b = x² / (0.2 – x)

Because x is tiny relative to 0.2, the approximation gives:

x ≈ √(6.61 × 10^-10 × 0.2) ≈ 1.15 × 10^-5 M

So:

• [OH^–] ≈ 1.15 × 10^-5 M
• pOH ≈ 4.94
• pH ≈ 9.06

If you solve exactly with the quadratic equation, the result is essentially the same to ordinary reporting precision. That is why the approximation is widely accepted for this type of weak-base salt calculation.

Quick comparison table for sodium butyrate concentration vs pH

The table below shows how the pH shifts with concentration at 25 C using pKa = 4.82. These values are realistic equilibrium estimates based on weak-base hydrolysis.

Sodium Butyrate Concentration (M)	Approximate [OH-] (M)	Approximate pOH	Approximate pH
0.010	2.57 × 10^-6	5.59	8.41
0.050	5.75 × 10^-6	5.24	8.76
0.100	8.13 × 10^-6	5.09	8.91
0.200	1.15 × 10^-5	4.94	9.06
0.500	1.82 × 10^-5	4.74	9.26
1.000	2.57 × 10^-5	4.59	9.41

What assumptions are being made?

When chemists solve a problem like this, several assumptions are usually built into the process:

• The sodium butyrate fully dissociates into ions in water.
• Activity effects are ignored, so concentrations are treated as ideal.
• The pKa value used is valid for the selected temperature, commonly 25 C.
• The hydroxide generated by butyrate hydrolysis is small compared with the formal concentration.
• Autoprotolysis of water contributes negligibly compared with hydrolysis under these conditions.

These assumptions are standard for undergraduate and applied chemistry calculations. In concentrated real-world formulations, especially where ionic strength matters, activity corrections may shift the observed pH slightly from the ideal textbook value.

Approximation vs exact quadratic solution

For weak acids and weak bases, students are often taught the square-root shortcut. It works when the extent of reaction is very small relative to the starting concentration. For 0.2 M sodium butyrate, that condition is satisfied very well. Still, it is useful to understand the exact method.

Starting from:

K_b = x² / (C – x)

Rearrange into standard quadratic form:

x² + K_bx – K_bC = 0

The physically meaningful root is:

x = (-K_b + √(K_b² + 4K_bC)) / 2

That gives the equilibrium hydroxide concentration directly. Because K_b is tiny and C is relatively large, the exact answer is almost identical to the square-root estimate.

Second comparison table: constants and thermal effects that influence the answer

Temperature affects pKw, and pKa values can vary slightly by source and conditions. The following table summarizes practical data used in pH estimation.

Parameter	Typical Value	Why It Matters
Butyric acid pKa at 25 C	About 4.82	Determines Ka, then Kb for butyrate
Ka of butyric acid	About 1.5 × 10^-5	Used to convert acid strength into conjugate base strength
Kb of butyrate at 25 C	About 6.6 × 10^-10	Controls how much OH- forms in water
pKw at 25 C	14.00	Needed to convert pOH to pH
pKw at 40 C	13.68	Shows why pH depends on temperature even with similar chemistry

Common mistakes when solving this problem

• Treating sodium butyrate like a strong base. It is not NaOH. The basicity comes from butyrate hydrolysis, so equilibrium is required.
• Using Ka directly as if the salt were an acid. The dissolved species is the conjugate base, so calculate Kb from Ka.
• Forgetting pOH. Since hydrolysis produces OH^–, find pOH first, then convert to pH.
• Ignoring temperature. If the problem specifies a non-25 C temperature, use the appropriate pKw.
• Using the wrong acid. Sodium butyrate comes from butyric acid, not acetic acid or propionic acid.

Why the pH is only mildly basic, not extremely high

This point is worth emphasizing. Even though the starting concentration is 0.2 M, the pH is around 9 rather than 12 or 13 because butyrate is only a weak base. Most butyrate ions remain unprotonated at equilibrium, and only a tiny fraction hydrolyzes to produce hydroxide. In fact, the percent hydrolysis is very small, on the order of only a few thousandths of a percent for this concentration. That is typical behavior for salts of weak acids with modest Kb values.

Practical relevance of sodium butyrate pH calculations

Sodium butyrate appears in biochemical research, fermentation studies, cell culture work, gastrointestinal research, and some specialty formulations. In these contexts, pH matters because it can affect:

• cell viability and buffer compatibility
• enzyme performance and reaction rates
• microbial growth conditions
• stability of combined ingredients in solution
• handling, storage, and target formulation design

If you are preparing laboratory solutions, remember that measured pH can differ slightly from the ideal calculated pH because of ionic strength, calibration, carbon dioxide absorption, and impurities in water or reagents. Still, the equilibrium calculation gives an excellent theoretical baseline.

Authoritative references for pH and acid-base equilibrium concepts

• Purdue University: Weak acid and weak base equilibrium problem solving
• Michigan State University: Acid-base equilibrium concepts
• NCBI Bookshelf: Clinical chemistry overview of pH and acid-base principles

Final answer

For a 0.2 M aqueous solution of sodium butyrate at 25 C, using pKa = 4.82 for butyric acid, the calculated pH is approximately 9.06. This result follows from converting the acid constant to the conjugate base constant, solving for hydroxide production by hydrolysis, and then converting from pOH to pH.

If you want to test different concentrations, pKa values, or temperatures, the calculator above updates the chemistry instantly and plots the pH trend visually.