Question

pH of 1 litre of HCL solution is 1. How much water (in litres) is added to make pH=2?

Answer 1

We are given that the pH of 1 liter of HCl solution is 1, and we need to determine how much water should be added to make the pH of the solution 2. 

Step 1: Understanding pH and concentration. The pH of a solution is related to the concentration of hydrogen ions (\( [H^+] \)) by the equation: \[ \text{pH} = -\log [H^+] \] For a pH of 1, the concentration of hydrogen ions is: \[ [H^+] = 10^{-\text{pH}} = 10^{-1} = 0.1 \, \text{M} \] So the initial concentration of HCl is 0.1 M in 1 liter of solution. 

Step 2: pH after dilution. When water is added, the concentration of hydrogen ions decreases, which increases the pH. For the final pH of 2, we need to find the new concentration of hydrogen ions: \[ \text{pH} = 2 \quad \Rightarrow \quad [H^+] = 10^{-2} = 0.01 \, \text{M} \] 

Step 3: Using dilution formula. The dilution formula relates the initial and final concentrations and volumes: \[ C_1 V_1 = C_2 V_2 \] Where: - \( C_1 \) is the initial concentration of HCl, - \( V_1 \) is the initial volume of HCl, - \( C_2 \) is the final concentration of HCl, - \( V_2 \) is the final volume of the solution. Substituting the known values: \[ 0.1 \times 1 = 0.01 \times V_2 \] Solving for \( V_2 \): \[ V_2 = \frac{0.1 \times 1}{0.01} = 10 \, \text{liters} \] 

Step 4: Amount of water added. The final volume is 10 liters, and the initial volume is 1 liter. So, the amount of water added is: \[ 10 - 1 = 9 \, \text{liters} \] 

Final Answer: The amount of water that should be added is \( \boxed{9} \) liters. 

Quick Tip: To dilute a solution and change its pH, you can use the dilution formula to calculate the required final volume based on the desired concentration.