For a 100 times increase in concentration of hydrogen ions, a) pH increases by 2 units, b) pH decreases by 2 units, c) pH remains unaltered, d) pH decreases by 1 unit.
The Correct Answer and Explanation is:
The correct answer is b) pH decreases by 2 units.
Explanation:
The pH scale is a measure of the hydrogen ion concentration in a solution, and it is logarithmic. This means that a 10-fold increase in the concentration of hydrogen ions results in a decrease of 1 pH unit. The formula for pH is:pH=−log[H+]\text{pH} = -\log[\text{H}^+]pH=−log[H+]
Where:
- [H+][\text{H}^+][H+] is the concentration of hydrogen ions in moles per liter.
If the concentration of hydrogen ions increases by a factor of 100 (which is 10²), this means:pH=−log[H+]andif [H+] increases by 100,\text{pH} = -\log[\text{H}^+] \quad \text{and} \quad \text{if} \, [\text{H}^+] \, \text{increases by 100,}pH=−log[H+]andif[H+]increases by 100,
The pH will decrease by 2 units. To understand this mathematically:
If the original concentration of hydrogen ions is [H+]=x[H^+] = x[H+]=x, then:pH=−log(x)\text{pH} = -\log(x)pH=−log(x)
Now, if the concentration increases 100 times, the new concentration is [H+]=100x[H^+] = 100x[H+]=100x, and the new pH is:New pH=−log(100x)=−log(100)−log(x)=−2−log(x)\text{New pH} = -\log(100x) = -\log(100) – \log(x) = -2 – \log(x)New pH=−log(100x)=−log(100)−log(x)=−2−log(x)
This shows that the pH decreases by 2 units when the concentration of hydrogen ions increases by a factor of 100.
Thus, for a 100 times increase in the concentration of hydrogen ions, the pH decreases by 2 units.
