Log scale intuition: Compared with a solution at pH 7, a solution at pH 5 is how much more acidic (in terms of hydrogen ion concentration)?

Introduction / Context:
The pH scale is logarithmic, so each unit change corresponds to a tenfold change in hydrogen ion concentration. Comfort with this idea is critical in biochemistry and environmental chemistry.

Given Data / Assumptions:

• pH = −log10[H+].
• Compare pH 5 to pH 7.
• Assume dilute aqueous conditions so activity ≈ concentration.

Concept / Approach:
A decrease of 1 pH unit means a tenfold increase in [H+]. Therefore, a decrease of 2 pH units (from 7 to 5) means a 10^2, or 100-fold, increase in [H+].

Step-by-Step Solution:
Compute [H+] at pH 7 → 10^-7 M. Compute [H+] at pH 5 → 10^-5 M. Ratio → 10^-5 / 10^-7 = 10^2 = 100. Thus, pH 5 is 100 times more acidic than pH 7.

Verification / Alternative check:
Graphing pH vs. [H+] on a log scale quickly confirms the tenfold-per-unit relationship.

Why Other Options Are Wrong:
Options A and B invert acidity/basicity; option C undervalues the two-unit change; option E ignores the fundamental logarithmic definition of pH.

Common Pitfalls:
Treating pH as linear; forgetting that a two-unit shift is 100-fold, not double.

Final Answer:
100 times more acidic.