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 pH scale
The pH scale measures the concentration of hydrogen ions (H⁺) in a solution. A lower pH value indicates a higher concentration of hydrogen ions, which means higher acidity.

### Step 2: Use the pH formula
The relationship between pH and hydrogen ion concentration is given by the formula:
\[ \text{pH} = -\log[H^+] \]
From this, we can derive the concentration of hydrogen ions:
\[ [H^+] = 10^{-\text{pH}} \]

### Step 3: Calculate [H⁺] for pH = 2
For a solution with pH = 2:
\[ [H^+] = 10^{-2} \, \text{mol/L} \]
This means the concentration of hydrogen ions is:
\[ [H^+] = 0.01 \, \text{mol/L} \]

### Step 4: Calculate [H⁺] for pH = 6
For a solution with pH = 6:
\[ [H^+] = 10^{-6} \, \text{mol/L} \]
This means the concentration of hydrogen ions is:
\[ [H^+] = 0.000001 \, \text{mol/L} \]

### Step 5: Find the ratio of the hydrogen ion concentrations
To find out how many times more acidic the pH = 2 solution is compared to the pH = 6 solution, we take the ratio of their hydrogen ion concentrations:
\[ \text{Ratio} = \frac{[H^+] \text{ at pH 2}}{[H^+] \text{ at pH 6}} = \frac{10^{-2}}{10^{-6}} \]

### Step 6: Simplify the ratio
This simplifies to:
\[ \text{Ratio} = 10^{-2 - (-6)} = 10^{4} = 10,000 \]

### Conclusion
Thus, a solution of pH = 2 is 10,000 times more acidic than a solution of pH = 6.

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