AIIMS 2017 Chemistry pH and Dilution MCQ Question

When the solution with a pH of 5 is diluted 100 times, the concentration of hydrogen ions $[H^+]$ decreases to $10^{-7} \, \text{M}$ due to the dilution, but the contribution of water's autoionization $[H^+] = 10^{-7} \, \text{M}$ must also be considered. This results in a total $[H^+] = 10^{-7} + 10^{-7} = 2 \times 10^{-7} \, \text{M}$. The pH can then be calculated using the formula $\text{pH} = -\log(2 \times 10^{-7})$, which simplifies to approximately 6.7, confirming option C.

Option A is incorrect because it neglects the contribution from the autoionization of water. Option B misrepresents the calculation of total $[H^+]$ without considering the logarithmic nature of pH. Option D is not applicable as it does not provide any relevant information.