Find the pH of water

Question

The ionization constant for water (kw) is 2.9 x 10^ -14 at 40 ^o C

What is the pH of water at this temperature?

Answer 1

There are three pieces of information we need to solve this problem.

1) The ionization constant for water (K_w) is expressed as: K_w = [H₃O⁺] [OH^-]

2) The concentration of H₃O⁺ and OH^- are the same in pure water since in order to form one ion, the other is formed by definition. In other words [H₃O⁺] [OH^-] = [H₃O⁺]² for pure water.

3) The formula for pH is: pH = - log [H₃O⁺]

We simply have to plug in the value given by the question, solve for [H₃O⁺], and then use this value in our pH equation.

1) K_w = [H₃O⁺] [OH^-]

2.9 x 10^-14 = [H₃O⁺] [OH^-]

2) 2.9 x 10^-14 = [H₃O⁺]²

square root both sides of the equation:

[H₃O⁺] = 1.7 x 10^-7

3) now insert it into our pH equation and solve:

pH = - log [H₃O⁺]

pH = - log (1.7 x 10^-7)

Answer: pH = 6.77