Question

The value of pH for a \(10^{-8}\,M\) HCl solution at \(25^\circ C\) is closest to:

• A. \(8\)
• B. \(7\)
• C. \(6.98\)
• D. \(6\)

Hint:

Whenever acid concentration approaches \(10^{-7}M\), never ignore the contribution of water. Directly using \(pH=-\log C\) gives incorrect results.

Answer 1

The Correct Option is C

Concept: When the concentration of strong acid becomes extremely small, the contribution of hydrogen ions from water auto-ionization cannot be neglected. Step 1: Write hydrogen ion concentration. For pure water: \[ [H^+]=10^{-7}M \] For HCl: \[ [H^+]=10^{-8}M \] Total hydrogen ion concentration: \[ [H^+]=10^{-7}+10^{-8} \] \[ =1.1\times10^{-7} \] Step 2: Calculate pH. \[ pH=-\log(1.1\times10^{-7}) \] \[ pH=7-\log(1.1) \] \[ pH=7-0.041 \] \[ pH\approx6.96 \] The nearest value among the options is: \[ 6.98 \] Hence option (C) is correct.