An analyst wants to convert $$1$$ L HCl of pH $$= 1$$ to a solution of HCl of pH $$= 2$$. The volume of water needed to do this dilution is _____ mL. (Nearest integer)

Hydrochloric acid (HCl) is a strong monobasic acid that dissociates completely in an aqueous solution.
Therefore, the molar concentration of hydronium ions [H+] is directly equal to the total molarity of the HCl solution (M).

The relationship between pH and hydrogen ion concentration is defined by the core logarithmic function:

$$[H^{+}] = 10^{−pH}$$

When a solution is diluted by adding a pure solvent (water), the total number of moles of solute remains invariant. This conservation of solute quantity is governed by the classical dilution law equation:

Where M1 and V1 represent the initial molar concentration and volume, and M2 and V2 represent the final molar concentration and volume post-dilution.

Step 1: Extract Initial Parameters
For the initial state of the hydrochloric acid solution:

• Initial Volume (V1) = 1 L = 1000 mL
• Initial pH = 1
• Initial Concentration (M1) = 10−1 M = 0.1 M

Step 2: Extract Target Parameters
For the final state following the dilution process:

• Target pH = 2
• Target Concentration (M2) = 10−2 M = 0.01 M

Step 3: Calculate Total Final Volume (V2)
Applying the values to the dilution principle formula:
(0.1 M) × (1000 mL) = (0.01 M) × V2
Rearranging the parameters algebraically to isolate and solve for V2:
V2 = 0.1 × 10000.01 = 10,000 mL
The total final volume of the solution must become 10,000 mL (which is equivalent to 10 L).

Step 4: Determine Added Solvent Volume (ΔV)
The net volume of extra water needed to expand the system is the absolute difference between the total final volume and the initial volume: