A solution with `pH = 2` is more acidic than one with a `pH = 6` by a factor of

Options

A. `4`
B. `12`
C. `400`
D. `10^(4)`

Explanation

To solve the problem of determining how much more acidic a solution with a pH of 2 is compared to a solution with a pH of 6, we can follow these steps:

### Step 1: Understand the pH scale
The pH scale is a logarithmic scale that measures the concentration of hydrogen ions (H⁺) in a solution. A lower pH value indicates a higher concentration of hydrogen ions, which means the solution is more acidic.

### Step 2: Calculate the H⁺ concentration for pH 2
Using the formula for pH:
\[ \text{pH} = -\log[H^+] \]

For a solution with pH = 2:
\[ 2 = -\log[H^+] \]
To find [H⁺], we take the antilog:
\[ [H^+] = 10^{-2} \]
So, the concentration of H⁺ ions in the solution with pH 2 is:
\[ [H^+] = 0.01 \, \text{mol/L} \]

### Step 3: Calculate the H⁺ concentration for pH 6
Using the same formula for pH:
For a solution with pH = 6:
\[ 6 = -\log[H^+] \]
Taking the antilog:
\[ [H^+] = 10^{-6} \]
So, the concentration of H⁺ ions in the solution with pH 6 is:
\[ [H^+] = 0.000001 \, \text{mol/L} \]

### Step 4: Determine the factor of acidity difference
To find out how many times more acidic the solution with pH 2 is compared to the solution with pH 6, we take the ratio of their H⁺ concentrations:
\[ \text{Factor} = \frac{[H^+] \text{ (pH 2)}}{[H^+] \text{ (pH 6)}} \]
Substituting the values:
\[ \text{Factor} = \frac{10^{-2}}{10^{-6}} \]
This simplifies to:
\[ \text{Factor} = 10^{-2 + 6} = 10^{4} \]

### Conclusion
Thus, a solution with pH = 2 is more acidic than one with pH = 6 by a factor of \( 10^4 \).

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