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?

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:

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