pH scale refresher: if the pH of an aqueous solution changes by exactly one unit, by what factor does the hydrogen ion concentration [H+] change?
-
A10
-
B20
-
C70
-
D100
-
E5
Answer
Correct Answer: 10
Explanation
Introduction / Context:The pH scale is logarithmic. Many quick diagnostics in water treatment, bioprocessing, and environmental engineering depend on translating pH changes into concentration changes. Remembering the factor associated with a one-unit change keeps order-of-magnitude reasoning sharp.
Given Data / Assumptions:
- Definition: pH = −log10[H+].
- Activity approximated by concentration in dilute aqueous solutions.
Concept / Approach:A one-unit change on a base-10 logarithmic scale corresponds to a tenfold change in the underlying quantity. Thus, if pH decreases by 1 (e.g., from 7.0 to 6.0), [H+] increases by a factor of 10. Conversely, if pH increases by 1, [H+] decreases by a factor of 10. The relationship is exact under the definition and the activity≈concentration approximation.
Step-by-Step Solution:
Start from pH = −log10[H+].Let pH change by 1: ΔpH = ±1.Then [H+] changes as 10^(−pH) → 10^(−(pH±1)) = 10^(∓1) * 10^(−pH).Therefore, the multiplicative factor is 10 (increase or decrease depending on direction).Verification / Alternative check:Example: pH 7.0 → [H+] = 10^−7 M; pH 6.0 → [H+] = 10^−6 M (tenfold larger).
Why Other Options Are Wrong:
- 20, 70, 100, 5 are not consistent with the base-10 logarithmic definition.
Common Pitfalls:Mixing percentage changes with multiplicative factors; on a log scale, additive changes in pH correspond to multiplicative changes in [H+].
Final Answer:10