4. What is the pH of a 1.0×1010 M aqueous solution of hydrochloric acid?
pH = –log[H3O+]; here [H3O+] is just slightly greater than 1.0×10–7 (the hydronium ion is mostly generated by the water, not the hydrochloric acid).
Comment: This type of pH problem occurs frequently on the contest exam. It challenges the student to critically examine the chemical reactivity, not just plug numbers into a calculator. For sufficiently concentrated strong acids, the pH is found from the acid concentration, which, in this case, would lead to the calculation: pH = –log(1.0×10–10) = 10.0, indicating a basic solution. This is counterintuitive to the presence of a strong acid. Most of the hydronium ion concentration arises from water, 1.0×10–7, and the small amount of hydrochloric acid present is not sufficient to change this concentration significantly. Thus, pH = –log(1.0×10–7) = 7.0 to the correct number of significant digits.