How many times a solution of pH = 2 has higher acidity than a solution of pH = 6 ?

Options

A. 10000
B. 12
C. 400
D. 4

Answer

To determine how many times a solution of pH = 2 has higher acidity than a solution of pH = 6, we can follow these steps:

### Step 1: Understand the relationship between pH and hydrogen ion concentration
The pH of a solution is related to the concentration of hydrogen ions \([H^+]\) in the solution by the formula:
\[ \text{pH} = -\log[H^+] \]

### Step 2: Calculate the hydrogen ion concentration for pH = 2
For a solution with pH = 2:
\[ [H^+] = 10^{-\text{pH}} = 10^{-2} \, \text{M} \]

### Step 3: Calculate the hydrogen ion concentration for pH = 6
For a solution with pH = 6:
\[ [H^+] = 10^{-\text{pH}} = 10^{-6} \, \text{M} \]

### Step 4: Compare the two concentrations
Now, we need to find out how many times the concentration of hydrogen ions in the pH = 2 solution is compared to the pH = 6 solution:
\[ \text{Ratio} = \frac{[H^+] \text{ at pH 2}}{[H^+] \text{ at pH 6}} = \frac{10^{-2}}{10^{-6}} = 10^{(-2) - (-6)} = 10^{4} = 10000 \]

### Conclusion
Thus, a solution of pH = 2 has 10,000 times higher acidity than a solution of pH = 6.

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