Solution:

To solve this problem, we need to understand the relationship between pH and the concentration of hydrogen ions (H+) in a solution. The pH scale is a logarithmic scale that measures the acidity or basicity of a solution. A pH of 1 is considered highly acidic, while a pH of 2 is slightly less acidic.

Step 1: Find the concentration of hydrogen ions in the initial solution
The pH of the initial solution is given as 1. The pH scale is defined as the negative logarithm of the concentration of hydrogen ions. Mathematically, we can express this relationship as:
pH = -log[H+]

Rearranging the equation, we can find the concentration of hydrogen ions:
[H+] = 10^(-pH)

Substituting the given pH value of 1, we find:
[H+] = 10^(-1) = 0.1 M

Therefore, the initial solution has a hydrogen ion concentration of 0.1 M.

Step 2: Find the concentration of hydrogen ions in the final solution
The pH of the final solution is given as 2. Using the same equation as before, we find:
[H+] = 10^(-pH)

Substituting the pH value of 2, we have:
[H+] = 10^(-2) = 0.01 M

Therefore, the final solution should have a hydrogen ion concentration of 0.01 M.

Step 3: Find the volume of water needed to dilute the initial solution
We can use the dilution formula to calculate the volume of water needed:
C1V1 = C2V2

Where:
C1 = initial concentration of the acid
V1 = initial volume of the acid (1 L)
C2 = final concentration of the acid (0.01 M)
V2 = final volume of the acid (1 L + V water)

Substituting the known values into the formula, we have:
(0.1 M)(1 L) = (0.01 M)(1 L + V water)

Simplifying the equation, we get:
0.1 L = 0.01 L + 0.01 M * V water

Rearranging the equation, we can solve for V water:
0.09 L = 0.01 M * V water

V water = (0.09 L) / (0.01 M) = 9 L

Therefore, 9 liters of water must be added to 1 liter of the initial solution to create an aqueous solution with a pH of 2.

Hence, the correct answer is option C) 9.0 L.