Need help finding the ph

Question

What is the pH at 25 ∘C of water saturated with CO2 at a partial pressure of 1.15 atm ? The Henry's law constant for CO2CO2 at 25 ∘C∘C is 3.1×10−2mol/L-atm. TheCO2 is an acidic oxide, reacting with H2O to form H2CO3.

Answer 1

C = KP

C = concentration = ?

K = Henrys constant = 3.1x10^-2 M/atm

P = partial presure = 1.15 atm

C = 3.1x10^-2 M/atm x 1.15 atm = 0.03588 M

CO₂ + H₂O ==> H₂CO₃

0.03588 M CO₂ = 0.03588 M H₂CO₃

Ka₁ H2CO3 = 4.3x10^-7 = [H⁺][HCO₃^-] / [H₂CO₃]

4.3x10^-7 = (x)(x) / 0.03588-x and assuming x is small relative to 0.03588 ignore it in denominator

x² = 1.54x10^-8

x = 1.24x10^-4 M (which is less than 0.4% of 0.03588 so above assumption was valid).

[H+] = 1.24x10^-4

pH = -log [H+]

pH = 3.91