---
title: "pH of mixture of three samples"
subject: "Water Supply Engineering"
chapter: 4
key: "semester_5/water_supply_engineering:ph-mix-b66"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/ph-mix-b66
site: BCT Engineering
---

# pH of mixture of three samples

Water Supply Engineering · Chapter 4: Quality of Water

- Asked in: 2066 Bhadra (old course)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/ph-mix-b66
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-4

## Question

700 ml of water sample A with pH of 6 is mixed with 300 ml of sample B with pH 7 and 500 ml of sample C with pH 8. Calculate the pH of the mixture of A, B and C.

## Short answer

Combine hydrogen-ion amounts from all three samples: final H+ = (700e-6 + 300e-7 + 500e-8)/1500 = 4.90e-7 mol/l. Taking the negative log gives pH = 6.31.

## Answer

The moles of H$^+$ in each sample add on mixing, so the final hydrogen-ion concentration is the volume-weighted average. Buffering is ignored.

| Sample | Volume (ml) | pH | $[H^+]$ (mol/l) | $V \times [H^+]$ (ml$\cdot$mol/l) |
|---|---|---|---|---|
| A | 700 | 6 | $10^{-6}$ | $7.0\times10^{-4}$ |
| B | 300 | 7 | $10^{-7}$ | $3.0\times10^{-5}$ |
| C | 500 | 8 | $10^{-8}$ | $5.0\times10^{-6}$ |

$$
\begin{aligned} [H^+]_{mix} &= \frac{7.0\times10^{-4} + 3.0\times10^{-5} + 5.0\times10^{-6}}{700+300+500} \\ &= \frac{7.35\times10^{-4}}{1500} = 4.90\times10^{-7}\ \text{mol/l} \end{aligned}
$$

$$
pH = -\log_{10}(4.90\times10^{-7}) = 6.31
$$

**Answer: pH of the mixture = 6.31.**

## Check yourself

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

1. What is the correct combination for three samples?
   A. Average of 6, 7 and 8
   B. Sum of V x [H+] divided by total volume
   C. Sum of V x pH divided by total volume
   D. Product of the [H+] values
   Answer: B. Moles of H+ add, so total V x [H+] is divided by total volume (1500 ml). (Key point: Three-sample mixing)

2. Which sample contributes most H+ moles?
   A. A (700 ml, pH 6)
   B. All equal
   C. B (300 ml, pH 7)
   D. C (500 ml, pH 8)
   Answer: A. A gives 7.0x10^-4, far above B (3.0x10^-5) and C (5.0x10^-6). (Key point: Sample A contribution)

3. What is the pH of the mixture?
   A. 7.00
   B. 6.31
   C. 6.00
   D. 6.80
   Answer: B. [H+] = 7.35x10^-4/1500 = 4.9x10^-7, so pH = 6.31. (Key point: Result)

## Related in Water Supply Engineering

- [pH of mixture: 700 ml pH 6 and 500 ml pH 8](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Aph-mix-c76) — Water Supply Engineering, chapter 4
- [pH of mixture: 400 ml pH 6 and 700 ml pH 8](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Aph-mix-c69) — Water Supply Engineering, chapter 4

## Related in other subjects

- [pH of acetic acid and NaOH mixture](https://www.bctengineer.com/question.md?key=semester_2%2Fengineering_chemistry%3Aph-acetic-naoh) — Engineering Chemistry, chapter 1