How many litres of water must be added to litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?[AIEEE-2013] a)2.0 Lb)9.0 Lc)0.1 Ld)0.9 LCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:

pH of HCl solution = 1

pH of final solution = 2

To find:

Amount of water to be added to the HCl solution

Solution:

Step 1: Calculate the concentration of H+ ions in the HCl solution

The pH of a solution is defined as the negative logarithm (base 10) of the concentration of H+ ions in the solution.

pH = -log[H+]

1 = -log[H+]

[H+] = 10^-1 = 0.1 M

Step 2: Calculate the concentration of H+ ions in the final solution

pH = -log[H+]

2 = -log[H+]

[H+] = 10^-2 = 0.01 M

Step 3: Calculate the difference in concentration of H+ ions between the two solutions

Change in [H+] = [H+]final - [H+]initial

Change in [H+] = 0.01 M - 0.1 M = -0.09 M

Step 4: Calculate the volume of water to be added to the HCl solution

As the concentration of H+ ions decreases by 0.09 M, the same amount of water should be added to the solution.

Volume of water = Change in [H+] / [H+] in water = 0.09 M / 0.1 M = 0.9 L

Therefore, 0.9 liters of water must be added to 1 liter of the HCl solution to create an aqueous solution with a pH of 2.

Answer: Option (d) 0.9 L

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