Multiple choice

The ${p}{H}$ of a $1$ lit solution is $2$. It is diluted with water till its ${p}{H}$ becomes $4$. How many litres of water is added?

  1. $99$
  2. $9$
  3. $999$
  4. $9.9$
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A Correct answer
Explanation

pH 2 means [H+] = 0.01 M. pH 4 means [H+] = 0.0001 M. Using M1V1 = M2V2: 0.01 * 1 = 0.0001 * V2. V2 = 100 liters. Water added = 100 - 1 = 99 liters.

AI explanation

By the logarithm definition of pH, an increase from 2 to 4 means the hydrogen ion concentration drops by a factor of 100. The initial amount of H+ ions in the 1 litre solution is 10^-2 moles, and the final concentration is 10^-4 M. Using the dilution formula M1V1 = M2V2, we have (10^-2)(1) = (10^-4)(V2), which gives V2 = 100 litres. The volume of water added is the final volume minus the initial volume, so 100 - 1 = 99 litres.

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