Final answer:
The pH of a 0.100 M solution of carbonic acid with a Ka value of 4.50 x 10⁻⁷ is calculated by setting up an equilibrium expression, solving for the concentration of hydrogen ions, and then finding the pH, which is approximately 4.17.
Step-by-step explanation:
Calculating the pH of a Carbonic Acid Solution
To calculate the pH of a 0.100 M solution of carbonic acid with a Ka value of 4.50 x 10⁻⁷, we can set up an equilibrium expression reflecting the dissociation of carbonic acid (H₂CO₃) into hydrogen ions (H+) and bicarbonate ions (HCO₃⁻).
H₂CO₃ → H+ + HCO₃⁻
Let 'x' be the concentration of H+ ions at equilibrium. Assuming that the concentration of carbonic acid remains at 0.100 M because 'x' will be very small relative to the initial concentration, we can write the equilibrium expression as follows:
Ka = [H+][HCO₃⁻] / [H₂CO₃]
4.50 x 10⁻⁷ = x² / 0.100
After solving for x, we find that:
x = √(4.50 x 10⁻⁷ * 0.100) = √(4.50 x 10⁻⁸) = 6.71 x 10⁻⁵
Now, we can calculate the pH:
pH = -log[H+] = -log(6.71 x 10⁻⁵) = 4.17
This means that the pH of the 0.100 M carbonic acid solution is approximately 4.17.