Acid–base scale — If the pH of an acidic solution is decreased from 5 to 2, by what factor does the hydrogen ion concentration [H+] increase?

Introduction / Context:
The pH scale is logarithmic, not linear. Every 1-unit change in pH corresponds to a tenfold change in hydrogen ion concentration [H+]. Understanding this is vital for analyzing acid strength, dosing neutralizing agents, and interpreting biological pH control. This question tests your ability to translate a pH change into the corresponding multiplicative change in [H+].

Given Data / Assumptions:

• Initial pH = 5; final pH = 2.
• Definition: pH = −log10[H+].
• Temperature is constant (so that the pH scale interpretation is consistent).

Concept / Approach:

Because pH is the negative base-10 logarithm of [H+], a drop in pH by ΔpH units multiplies [H+] by 10^(ΔpH). Here, the decrease from 5 to 2 is 3 units, so [H+] increases by 10^3. This exponential nature explains why small pH shifts can have large chemical or biological effects.

Step-by-Step Solution:

Verification / Alternative check:

Directly from the definition: change in pH = −log10([H+]_2) + log10([H+]_1) = log10([H+]_1/[H+]_2). Rearranging gives [H+]_2/[H+]_1 = 10^(pH_1 − pH_2) = 10^(5 − 2) = 10^3.

Why Other Options Are Wrong:

10 or 100: These correspond to 1- or 2-unit changes, respectively. 10000 would require a 4-unit change. “Unchanged” is incorrect because pH changed significantly.

Common Pitfalls:

Treating pH changes linearly; forgetting that lower pH means higher [H+]; mixing up pH and pOH relationships (pH + pOH = 14 at 25°C).

Final Answer:

1000