How many times stronger is the hydrogen-ion concentration of a pH 4 solution as compared with a pH 9 solution?
A.
0.00001
B.
5
C.
100,000
D.
50
The Correct answer and Explanation is:
To determine how many times stronger the hydrogen-ion concentration of a pH 4 solution is compared to a pH 9 solution, we need to understand the pH scale and its logarithmic nature.
The pH scale measures the acidity or alkalinity of a solution based on the concentration of hydrogen ions (H⁺). The scale ranges from 0 to 14, with lower values indicating higher acidity (more H⁺ ions) and higher values indicating more basicity (fewer H⁺ ions). The pH value is calculated using the formula:pH=−log[H+]\text{pH} = -\log[\text{H}^+]pH=−log[H+]
Because the pH scale is logarithmic, each whole number change in pH corresponds to a tenfold change in hydrogen-ion concentration. For example, a solution with a pH of 3 has ten times more H⁺ ions than a solution with a pH of 4.
To compare the hydrogen-ion concentrations of pH 4 and pH 9 solutions, we calculate the difference in pH values:ΔpH=9−4=5\Delta \text{pH} = 9 – 4 = 5ΔpH=9−4=5
Since each unit on the pH scale represents a tenfold difference, a change of 5 pH units means:105=100,00010^5 = 100,000105=100,000
This calculation shows that the hydrogen-ion concentration of the pH 4 solution is 100,000 times stronger than that of the pH 9 solution.
The correct answer is:
C. 100,000
Explanation
A pH 4 solution is 100,000 times more acidic than a pH 9 solution because the pH scale is logarithmic, meaning that each unit difference represents a tenfold change in hydrogen-ion concentration. A decrease in pH indicates an increase in acidity, and as the pH drops from 9 to 4, the solution becomes progressively more acidic. The factor of 100,000 highlights how dramatically acidity can change even with relatively small shifts in pH. Understanding this logarithmic relationship is essential in fields like chemistry, biology, and environmental science, where pH plays a crucial role in chemical reactions and biological processes.