#2H_2O rightleftharpoons H_3O^+ + OH^-#

The auto-ionization constant of water is given by:

#K_W = [ H_3O^+] [ OH^-]#

Apply the #log# function to both sides of the equation:

#log(K_W )=log( [ H_3O^+] [ OH^-])#

#log(K_W )= log[ H_3O^+] + log[ OH^-]#

Multiply both sides of the equation by a negative sign

#-{log(K_W )}= -{\ log[ H_3O^+] + log[ OH^-]\ }#

# -log(K_W )= -log[ H_3O^+] - log[ OH^-]#

# -log(1.0xx10^-14)= -log[ H_3O^+] - log[ OH^-]#

# 14 = -log[ H_3O^+] - log[ OH^-]#

#pH = -log[ H_3O^+] " and " pOH= - log[ OH^-] #

#14 = pH + pOH =>#

#pH + pOH = 14#