Water Chemistry – Comparing Acidity Using pH (Logarithmic Scale) Two water samples have pH values: Sample A = 4.4 and Sample B = 6.4. By how many times is Sample A more acidic than Sample B?

Introduction / Context:
pH is a logarithmic measure of hydrogen ion activity in water and is central to environmental engineering and water chemistry. Because the pH scale is logarithmic (base 10), small numerical differences in pH represent large multiplicative changes in acidity. This question checks whether you can translate a pH difference into a ratio of acidities for two samples.

Given Data / Assumptions:

• Sample A: pH_A = 4.4.
• Sample B: pH_B = 6.4.
• Definition: pH = −log10[H+].
• Temperature and activity corrections are ignored for this comparison (standard classroom assumption).

Concept / Approach:

The concentration of hydrogen ions is related to pH by [H+] = 10^(−pH). The relative acidity (how many times more acidic one sample is than another) is the ratio of their [H+] values. Since logs subtract, a difference of 1.0 pH unit corresponds to a 10-fold change in acidity; a difference of 2.0 pH units corresponds to a 100-fold change, and so on.

Step-by-Step Solution:

Verification / Alternative check:

Because the pH difference is exactly 2.0 units (6.4 − 4.4), the ratio must be 10^2 = 100. This rule of thumb (each pH unit is a factor of 10) is widely used for quick comparisons without detailed calculations.

Why Other Options Are Wrong:

• 0: Would imply identical acidity, which is impossible with different pH values.
• 50 and 200: Do not match the exact logarithmic relationship for a 2.0 pH-unit difference; only 100 is correct.

Common Pitfalls:

Confusing the logarithmic scale with a linear one, or reversing the direction (thinking higher pH means more acidic). Remember that lower pH means higher [H+].

Final Answer:

100