Define pH. Derive the equation [H+]=[OH-]

DEFINITION: 

“The pH of a solution is defined as the negative of the logarithm of the hydrogen ion concentration”

MATHEMATICAL EXPRESSION:

 In mathematical terms: pH= -log[H+]

DERIVATION: 

The equation for the ionization of water is: H2OàH+ + OH-……….(eq 1)

The expression for the equilibrium constant for this reaction is:

K=[H+] [OH-] / [H2O] or K[H2O]= [H+][OH-]……..(eq 2)

Since dissociation of water into ions is very small, therefore the concentration of H2O remains constant. As, K[H2O]=Kw , So equation 2 can be written as Kw=[H+][OH-]……(eq3)

This new constant is called dissociation constant of water. The value of Kw of water at 25 degree is 1.0^-14.

Thus equation 3 can be written as: Kw= [H+][OH-]=1.0^-14 ………(eq4)

CONCLUSION: 

Since one H+ ion is produced for every OH- ion , therefore, the concentration of H+ ion will be equal to the concentration of OH- ions i-e [H+]=[OH-]. This fact help us to calculate the concentration of H+ or OH- ions, which comes out to be 1.0^-7 mol/L. Any solution in which [H+]={OH-] is known as neutral solution.