---
title: "Buffer capacity and range; sodium benzoate concentration"
subject: "Engineering Chemistry"
chapter: 1
key: "semester_2/engineering_chemistry:buffer-capacity-range"
source: https://www.bctengineer.com/q/semester_2/engineering_chemistry/buffer-capacity-range
site: BCT Engineering
---

# Buffer capacity and range; sodium benzoate concentration

Engineering Chemistry · Chapter 1: Electro-chemistry and Buffer

- Asked in: 2071 Bhadra, 2+3 marks
- Video: [Henderson-Hasselbalch Equation Explained | pH & Buffer Example Problem](https://www.youtube.com/watch?v=Y3htAlEOFv0) — Chemistry TowleVision
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/engineering_chemistry/buffer-capacity-range
- Whole chapter: https://www.bctengineer.com/md/semester_2/engineering_chemistry/chapter-1

## Question

Define buffer capacity and buffer range. Calculate the concentration of sodium benzoate that must be present in 0.1 M benzoic acid to make a buffer solution of pH 3.7 (Ka for benzoic acid is 1.8×10⁻⁴).

## Short answer

Buffer capacity is the moles of strong acid or base needed to change the pH of 1 L buffer by one unit. Buffer range is pH ≈ pKa ± 1 for an acidic buffer. Using pH = pKa + log([salt]/[acid]), [sodium benzoate] = 0.090 M.

## Answer

#### Buffer capacity
The number of moles of strong acid or base needed to change the pH of 1 L of buffer by one unit. It is highest when [salt] = [acid] and when the concentrations are large.

#### Buffer range
The pH range over which a buffer works effectively. It is about **pKa ± 1** for an acidic buffer (i.e. when [salt]/[acid] lies between 0.1 and 10), and pOH = pKb ± 1 for a basic buffer.

#### Calculation
```text
pH = 3.7  →  [H⁺] = 10⁻³·⁷ = 2.0×10⁻⁴ M
[H⁺] = Ka [acid]/[salt]
[salt] = Ka [acid]/[H⁺]
       = 1.8×10⁻⁴ × 0.1 / 2.0×10⁻⁴
       = 0.090 M
```
Check with Henderson: pKa = 3.745; log([salt]/[acid]) = 3.7 − 3.745 = −0.045, so ratio = 0.90 and [salt] = 0.090 M.

**Answer: [sodium benzoate] ≈ 0.09 M.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The effective range of an acidic buffer is about:
   A. pKa ± 5
   B. pH 0 to 14
   C. pKa ± 0.01
   D. pKa ± 1
   Answer: D. Ratio of salt to acid between 0.1 and 10 gives pH = pKa ± 1. (Key point: Buffer range)

2. Buffer capacity is highest when:
   A. [salt] is 100 times [acid]
   B. concentrations are very low
   C. pH is 7
   D. [salt] = [acid] and concentrations are large
   Answer: D. Equal components and high concentrations give maximum capacity. (Key point: Factors for high capacity)

3. Which formula gives [salt] from pH?
   A. [salt] = [H+][acid]/Ka
   B. [salt] = Ka [H+]/[acid]
   C. [salt] = [acid]/(Ka [H+])
   D. [salt] = Ka [acid]/[H+]
   Answer: D. From [H+] = Ka [acid]/[salt]. (Key point: Formula for salt)

4. pH 3.7, Ka = 1.8x10^-4, acid 0.1 M. [salt] is about:
   A. 0.18 M
   B. 0.9 M
   C. 0.01 M
   D. 0.09 M
   Answer: D. [H+] = 2.0x10^-4; [salt] = 1.8x10^-4 x 0.1/2.0x10^-4 = 0.09 M. (Key point: Result)

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