This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Hey Temi, good to see you again. The value of K_w = 1.0 × 10^-14 at 25^ C comes from the autoionization of water. Step 1: Water undergoes a slight autoionization, meaning it reacts with itself to form hydronium ions (H_3O^+ or simply H^+) and hydroxide ions (OH^-). H_2O(l) + H_2O(l) H_3O^+(aq) + OH^-(aq) This can be simplified as: H_2O(l) H^+(aq) + OH^-(aq) Step 2: The equilibrium constant for this reaction is called the ion product of water, K_w. K_w = [H^+][OH^-] Step 3: In pure water at 25^ C, the concentrations of H^+ and OH^- ions are equal because they are produced in a 1:1 ratio. Through experimental measurements (e.g., conductivity), it's found that the concentration of each ion is 1.0 × 10^-7 M. [H^+] = 1.0 × 10^-7 M [OH^-] = 1.0 × 10^-7 M Step 4: Substitute these concentrations into the K_w expression. K_w = (1.0 × 10^-7)(1.0 × 10^-7) K_w = 1.0 × 10^(-7) + (-7) K_w = 1.0 × 10^-14 Thus, at 25^ C, the ion product of water is K_w = 1.0 × 10^-14. Send me the next one 📸