While calculating the `pH` of `10^(-7)M HCl`, the common ion effect of `HCl` on water is considered. Why the common ion effect of HCl on water is considered?

Explanation

a. Let the `K_(w)` of `H_(2)O = 10^(-10)` at `25^(@)C`. Then in pure water `[H_(3)O^(o+)] = [overset(Θ)OH] = 10^(5) = x`.
Thus, `[H_(3)O^(o+)]` from water in the presence of `10^(-7)M HCI` using the same value of `Kw` is:
`(x +10^(-7))x = 10^(-10)`
`:. x = 0.995 xx 10^(-5)M`
The percentage decrease in the concentration of `H_(3)O^(o+)` of water is:
`((10^(-5)-0.995 xx 10^(-5)))/(10^(-5)) xx 100 = 0.5%`
b. When the `K_(w)` of water was `10^(-14)`, the `H_(3)O^(o+)` concentration of pure water was `10^(-7)M` while that in the presence of `10^(-7) M HCI` was `0.618 xx 10^(-7)M` (refersection `8.45`, method `II`).
Therefore, the precentage decrease in the concentration of `H_(3)O^(o+)` of water in the presence of `10^(-7)M HCI` is:
`((10^(-7)-0.618xx10^(-7)))/(10^(-7)) xx 100 = 38.2%`
Thus, it can be concluded that the large the value of equilibrium constant of the week electrolyte, the lesser is the common ion effect produced. So, the common ion effect is experienced more by the weak electrolyte (having smaller equilibrium constant) than the strong electrolyte (having large equili-brium constant).