Which of the following solutions has the highest pH? (A) 1.0 mol L^{-1} acetic acid (B) 0.10 mol L^{-1} acetic acid (C) 1.0 mol L^{-1} hydrochloric acid (D) 0.10 mol L^{-1} hydrochloric acid - HSC - SSCE Chemistry - Question 13 - 2015 - Paper 1

To determine which solution has the highest pH, we need to consider the concentration and strength of the acids involved.

1. Acetic Acid: It is a weak acid, and its dissociation in water is represented as:

   $ext{CH}_3 ext{COOH} \rightleftharpoons \text{CH}_3 ext{COO}^- + \text{H}^+$

   For acetic acid, with a dissociation constant ( $K_a$) of approximately $1.8 \times 10^{-5}$, we can find the pH using the formula:

   $pH = -\log[H^+]$

   • For 1.0 mol L^{-1} acetic acid:

     Using the approximation, we can assume that $[H^+] \approx \sqrt{K_a \times C}$ where ( C ) is the molarity of the acid.

   • For 0.10 mol L^{-1} acetic acid:

     Similarly, we compute the $[H^+] = \sqrt{1.8 \times 10^{-5} \times 0.1}$.

2. Hydrochloric Acid: It is a strong acid and dissociates completely in water:

   $\text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-$

   • For 1.0 mol L^{-1} hydrochloric acid, the pH is:

   $pH = -\log[1.0] = 0$

   • For 0.10 mol L^{-1} hydrochloric acid, the pH is:

   $pH = -\log[0.1] = 1$

3. Comparative Analysis: To find the highest pH:

   • 1.0 mol L^{-1} acetic acid has a lower pH due to its weak nature.
   • 0.10 mol L^{-1} acetic acid has a higher pH compared to 1.0 mol L^{-1} hydrochloric acid.
   • 0.10 mol L^{-1} hydrochloric acid has a pH of 1, which is still lower than the acetic acid solution's pH.

Based on this analysis, the solution with the highest pH is (B) 0.10 mol L^{-1} acetic acid.