In this problem, we will use material balance and charge balance concepts to calculate the equilibrium concentrations in an extremely dilute solution of a strong acid, 1.0 x 10^-7 M HCl(aq).

(a) Write down the material balance equation for 1.0 x 10^-7 M HCl(aq), assuming that HCl ionizes completely in aqueous solution.

(b) Write down the charge balance equation (an electroneutrality condition) for this solution.

(c) Use the material balance and charge balance equations, and the ion product for water, K_w = [H₃O⁺][OH^-], to show that [H₃O⁺]² - c_o[H₃O⁺] - K_w = 0, where c_o = 1.0 x 10^-7 M.

(d) Use the quadratic formula to solve the equation in (c) for [H₃O⁺].

(e) Calculate [OH^-] and compare this value with [Cl^-].

What conclusion can you draw from this comparison?