Q.ii. Define pH and pOH. Derive relationship between pH and pOH.

Because [H+] and [OH-] in aqueous solutions span an enormous range (roughly 1 M down to about $10^{-14}$ M), it is far more convenient to work on a logarithmic scale. pH is defined as $pH=-\log_{10}[H^+]$, and pOH similarly as $pOH=-\log_{10}[OH^-]$; each single pH unit represents a ten-fold change in [H+]. The two are linked through water's own ionization equilibrium, $H_2O(l)+H_2O(l)\rightleftharpoons H_3O^+(aq)+OH^-(aq)$, whose equilibrium constant, the ionic product of water $K_w=[H_3O^+][OH^-]$, equals $1.0\times10^{-14}$ at 298 K (rising at higher temperature, since water's ionization is endothermic). Taking logarithms of $K_w=[H_3O^+][OH^-]$ gives the compact and very widely used relation $pH+pOH=14$ at 298 K. This immediately fixes the three regions of the pH scale: a neutral solution (pure water) has $[H_3O^+]=[OH^-]=1.0\times10^{-7}$ M and pH exactly 7; an acidic solution has $[H_3O^+]>[OH^-]$ and pH below 7; a basic solution has $[H_3O^+]<[OH^-]$ and pH above 7. Real-world reference points span this whole scale -- gastric juice sits near pH 2, blood is tightly held between 7.36 and 7.42, and even shifting blood pH by just 0.2 units can be dangerous, which is exactly why buffer systems (a separate concept) exist to hold biological pH steady.