Question

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The pH scale is arithmetic.
Reason R: Two solutions differing in one pH unit means that one solution is having ten times the hydrogen ($H^+$) ion concentration of the other.

• A. Both A and R are correct but R is NOT the correct explanation of A
• B. A is correct but R is incorrect
• C. A is incorrect but R is correct
• D. Both A and R are correct and R is the correct explanation of A

Hint:

Logarithmic scales are common in science:
- pH scale for acidity ($10\times$ difference per unit).
- Richter scale for earthquakes ($32\times$ energy difference per unit).
- Decibel scale for sound.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The pH scale is a chemical measurement used to express the acidity or alkalinity of an aqueous solution.
It is mathematically defined based on the concentration of hydrogen ions ($H^{+}$) present in the solution.

Step 2: Detailed Explanation:
Let us analyze both statements:
Assertion A: This statement asserts that the pH scale is arithmetic.
This is mathematically incorrect. The pH is defined as the negative logarithm (base 10) of the hydrogen ion activity (or concentration):
\[ \text{pH} = -\log_{10}[H^{+}] \]
Because it uses a logarithmic scale, a change of one unit on the pH scale represents a tenfold change in $[H^{+}]$. It is not a linear or arithmetic scale.
Reason R: This statement asserts that a difference of one pH unit means one solution has ten times the hydrogen ion concentration of the other.
This is correct. For example:
If Solution A has a pH of 5, then $[H^{+}]_{A} = 10^{-5}\text{ M}$.
If Solution B has a pH of 6, then $[H^{+}]_{B} = 10^{-6}\text{ M}$.
Comparing the two, Solution A has ten times more hydrogen ions than Solution B:
\[ \frac{10^{-5}}{10^{-6}} = 10 \]
Therefore, Assertion A is false, while Reason R is true.

Step 3: Final Answer:
Assertion A is incorrect, but Reason R is correct, which corresponds to Option (C).