---
title: "How many times more acidic: pH 6.5 and 7.8"
subject: "Water Supply Engineering"
chapter: 4
key: "semester_5/water_supply_engineering:ph-acidic-j66"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/ph-acidic-j66
site: BCT Engineering
---

# How many times more acidic: pH 6.5 and 7.8

Water Supply Engineering · Chapter 4: Quality of Water

- Asked in: 2066 Jestha (old course)
- Video: [pH of Water Calculation - Problem 8 Environmental Engineering GATE Civil Engineering](https://www.youtube.com/watch?v=8KRStkEbPcI) — Ekeeda GATE & ESE
- 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-acidic-j66
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-4

## Question

If there are two samples P and Q from the different treatment plants having the pH values of 6.5 and 7.8, calculate how many times the sample is acidic than sample B [sic].

## Short answer

Sample P (pH 6.5) is about 20 times more acidic than sample Q (pH 7.8) because hydrogen ion concentration ratio is 10^(1.3) ≈ 20.

## Answer

Acidity is measured by the hydrogen-ion concentration, $[H^+] = 10^{-pH}$. The pH scale is logarithmic, so each unit of pH changes $[H^+]$ ten times. (The question compares the two samples, P with pH 6.5 and Q with pH 7.8; "sample B" is read as sample Q.)

$$
\begin{aligned} [H^+]_P &= 10^{-6.5} = 3.162\times10^{-7}\ \text{mol/l} \\ [H^+]_Q &= 10^{-7.8} = 1.585\times10^{-8}\ \text{mol/l} \end{aligned}
$$

$$
\frac{[H^+]_P}{[H^+]_Q} = 10^{7.8-6.5} = 10^{1.3} = 19.95
$$

**Answer: Sample P (pH 6.5) is about 20 times more acidic than sample Q (pH 7.8).**

## Check yourself

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

1. How does [H+] change for one unit fall in pH?
   A. Doubles
   B. Ten times higher
   C. One unit higher
   D. Ten units higher
   Answer: B. pH is logarithmic, so each unit changes [H+] tenfold. (Key point: Log scale)

2. How many times more acidic is P (6.5) than Q (7.8)?
   A. About 20 (10^1.3)
   B. 1.3
   C. About 13
   D. About 1.2
   Answer: A. Ratio = 10^(7.8-6.5) = 10^1.3 = 19.95. (Key point: Ratio)

## Related in Water Supply Engineering

- [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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- [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

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