Ion product of water

The Ion product of water:

In the study of acid-base reactions, the hydrogen ion concentration is key; its value indicates the acidity or basicity of the solution. Because only a very small fraction of water molecules are ionized, the concentration of water, [H₂O], remains virtually unchanged (concentration of pure water, [H₂O] = 55.5M). Therefore, the equilibrium constant for the auto-ionization of water, according to Equation is:

Because we use H⁺(aq) and H₃O⁺(aq) interchangeably to represent the hydrated proton, the equilibrium constant can also be expressed as:

                                                          

To indicate that the equilibrium constant refers to the auto-ionization of water, we replace K_c by K_w:

                                              

Where K_w is called the ion-product constant, which is the product of the molar concentrations of H⁺ and OH^- ions at a particular temperature:

In pure water at 25°C, the concentrations of H⁺ and OH^- ions are equal and found to be [H⁺] =1.0x10²⁷ M and [OH]= 1.0x10²⁷M. Thus, at 25°C:

Whether we have pure water or an aqueous solution of dissolved species, the following relation always holds at 25°C:

Whenever [H⁺]=[OH^-], the aqueous solution is said to be neutral. In an acidic solution there is an excess of H⁺ ions and [H⁺]>[OH^-]. In a basic solution there is an excess of hydroxide ions, so [H⁺]<[OH^-]. In practice we can change the concentration of either H⁺ or OH- ions in solution, but we cannot vary both of them independently. If we adjust the solution so that [H⁺]=1.0x10^-6 M, the OH^- concentration must change to: