How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2? (1) 0.9 L (2) 2.0 L (3) 9.0 L (4) 0.1 L

To determine how many liters of water need to be added to dilute an aqueous solution of hydrochloric acid (HCl) from a pH of 1 to a pH of 2, we first need to understand the relationship between pH, hydrogen ion concentration, and dilution.

Understanding pH and Hydrogen Ion Concentration

The pH scale measures the acidity or basicity of a solution, with lower values indicating higher acidity. The formula for calculating pH is:

pH = -log[H⁺]

Here, [H⁺] represents the concentration of hydrogen ions in moles per liter (M). A pH of 1 corresponds to a hydrogen ion concentration of:

[H⁺] = 10^-1 M = 0.1 M

Calculating the Required Concentration

To find the concentration of hydrogen ions at a pH of 2, we use the same formula:

[H⁺] = 10^-2 M = 0.01 M

Setting Up the Dilution Equation

We start with 1 liter of the original solution, which has a concentration of 0.1 M. When we dilute this solution, the total volume will increase, and we need to find out how much water to add to achieve a final concentration of 0.01 M.

The dilution equation is:

C₁V₁ = C₂V₂

• C₁ = initial concentration (0.1 M)
• V₁ = initial volume (1 L)
• C₂ = final concentration (0.01 M)
• V₂ = final volume (unknown)

Calculating Final Volume

Substituting the known values into the equation gives:

0.1 M × 1 L = 0.01 M × V₂

Solving for V₂:

V₂ = (0.1 M × 1 L) / 0.01 M = 10 L

Finding the Volume of Water to Add

Now that we know the final volume must be 10 liters, we can find out how much water to add:

Volume of water to add = V₂ - V₁ = 10 L - 1 L = 9 L

Conclusion

Therefore, to dilute the solution from a pH of 1 to a pH of 2, you must add 9.0 liters of water. The correct answer is (3) 9.0 L.