of an acid and a base, respectively. In case of a conjugate acid-base pair, they are related in a simple manner so that if one is known, the other can be deduced. Considering the example of NH + and NH we see, NH + (aq) + H O(l) H O + (aq) + NH (aq) K a = [H O + ][ NH ] / [NH + ] = . × – NH (aq) + H O(l) NH + (aq) + OH – (aq) K b =[ NH + ][ OH – ] / NH = .
× – Net: H O(l) H O + (aq) + OH – (aq) K w = [H O + ][ OH – ] = . × – M Where, K a represents the strength of NH + as an acid and K b represents the strength of NH as a base. It can be seen from the net reaction that the equilibrium constant is equal to the product of equilibrium constants K a and K b for the reactions added. Thus, K a × K b = {[H O + ][ NH ] / [NH + ]} × {[NH + ] [OH – ] / [NH ]} = [H O + ][OH – ] = K w = ( .
× – ) × ( . × – ) = . × – M This can be extended to make a generalisation. The equilibrium constant for a net reaction obtained after adding two (or more) reactions equals the product of the equilibrium constants for individual reactions: K NET = K × K × …… ( .
) Similarly, in case of a conjugate acid-base pair, K a × K b = K w ( . ) Knowing one, the other can be obtained. It should be noted that a strong acid will have a weak conjugate base and vice-versa. Alternatively, the above expression K