A solution with a pH of 3 has a hydrogen ion concentration that is how many times greater than a solution with a pH of 5?

Question

Accepted Answer

100 times greater. The pH scale is logarithmic, meaning each unit represents a tenfold change in hydrogen ion concentration. pH is defined as -log[H⁺], so a pH of 3 corresponds to [H⁺] = 10⁻³ M and a pH of 5 corresponds to [H⁺] = 10⁻⁵ M. The difference is 2 pH units, which corresponds to 10² = 100 times. Therefore, the solution with pH 3 has a hydrogen ion concentration 100 times greater than the solution with pH 5.

A factor of 2 would apply if the pH scale were linear, but it is logarithmic. A factor of 10 would correspond to a difference of only 1 pH unit, not the 2-unit difference in this problem. A factor of 1000 would correspond to a 3-unit difference in pH (10³ = 1000). Understanding the logarithmic nature of the pH scale is crucial for correctly interpreting the magnitude of differences in acidity between solutions.

The pH scale typically ranges from 0 to 14, with values below 7 being acidic (higher [H⁺]), values above 7 being basic (lower [H⁺]), and a pH of exactly 7 being neutral (in pure water at 25°C). Understanding pH calculations, the relationship between [H⁺] and [OH⁻], the ion product of water (Kw = 1.0 × 10⁻¹⁴ at 25°C), and the properties of acids and bases is essential for the CLEP Chemistry exam. Being comfortable with logarithmic calculations is necessary for working pH problems.

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