The hydrogen ion concentration of a aqueous solution of at () is mathematically derived to be: — Ionic Equilibrium Chemistry Question

💡 Solution & Explanation

For very dilute acids ($C < 10^{-6} \text{ M}$), auto-ionization of water cannot be ignored. Let water contribute $x \text{ M }$ of $H^+$. Then total $[H^+] = x + 10^{-8}$. At equilibrium, $[H^+][OH^-] = (x + 10^{-8})(x) = 10^{-14}$. Solving this quadratic equation $x^2 + 10^{-8}x - 10^{-14} = 0$ yields $x \approx 0.95 \times 10^{-7} \text{ M}$. Total $[H^+] = 0.95 \times 10^{-7} + 0.1 \times 10^{-7} = 1.05 \times 10^{-7} \text{ M}$.