---
title: "pH of mixture: 400 ml pH 6 and 700 ml pH 8"
subject: "Water Supply Engineering"
chapter: 4
key: "semester_5/water_supply_engineering:ph-mix-c69"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/ph-mix-c69
site: BCT Engineering
---

# pH of mixture: 400 ml pH 6 and 700 ml pH 8

Water Supply Engineering · Chapter 4: Quality of Water

- Asked in: 2069 Chaitra, 4 marks
- 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-c69
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-4

## Question

If 400 ml of water with a pH of 6 is mixed with 700 ml of water with a pH of 8, what will be the resultant pH of the mixture?

## Short answer

Combine hydrogen-ion amounts: final H+ = (400e-6 + 700e-8)/1100 = 3.70e-7 mol/l. Taking the negative log gives pH = 6.43.

## Answer

pH $=-\log_{10}[H^+]$. On mixing, the moles of H$^+$ add, so the mixture's $[H^+]$ is the volume-weighted average (buffering is ignored).

$$
\begin{aligned} [H^+]_{mix} &= \frac{400\times10^{-6} + 700\times10^{-8}}{400+700} \\ &= \frac{4.0\times10^{-4} + 7.0\times10^{-6}}{1100} = 3.70\times10^{-7}\ \text{mol/l} \end{aligned}
$$

$$
pH = -\log_{10}(3.70\times10^{-7}) = 6.43
$$

**Answer: pH of the mixture = 6.43.**

## Check yourself

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

1. Why is pH not averaged directly (6 and 8 to 7)?
   A. Volumes cancel out
   B. Average pH is always right
   C. pH cannot be measured
   D. pH is logarithmic; [H+] must be averaged
   Answer: D. pH = -log[H+], so the average must be taken on [H+]. (Key point: Averaging)

2. Which expression gives [H+] of the mixture?
   A. (400x10^-6 + 700x10^-8)/1100
   B. (6x400 + 8x700)/1100
   C. (10^-6 + 10^-8)/2
   D. (400x10^-8 + 700x10^-6)/1100
   Answer: A. Each [H+] is weighted by its own volume and divided by total volume. (Key point: Formula)

3. The mixture [H+] is 3.7x10^-7. What is its pH?
   A. 7.57
   B. 7.00
   C. 6.00
   D. 6.43
   Answer: D. -log10(3.7x10^-7) = 6.43. (Key point: Final pH)

## 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 of three samples](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Aph-mix-b66) — Water Supply Engineering, chapter 4

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