Determine the pH of natural rainwater if the concentration of CO2 in the atmosphere is 390 ppm at 25ºC and 1 atm.

To determine the pH of natural rainwater, we need to understand that rainwater is naturally acidic due to the presence of CO2 in the atmosphere. When CO2 dissolves in water, it forms carbonic acid (H2CO3), which can dissociate to form hydrogen ions (H+), bicarbonate (HCO3-) and carbonate (CO3 2-) ions. The pH of the solution is then determined by the concentration of H+ ions.

Here are the steps to calculate the pH:

1. Convert the concentration of CO2 from ppm to mol/L. 1 ppm CO2 is approximately 0.0004 mol/L at 25ºC and 1 atm.

2. Write the chemical equation for the reaction of CO2 with water: CO2 + H2O ↔ H2CO3 ↔ H+ + HCO3-

3. Use the equilibrium constant (Ka) for the reaction. For carbonic acid, Ka1 = 4.45 x 10^-7 and Ka2 = 4.69 x 10^-11 at 25ºC.

4. Since the concentration of CO2 is much higher than the concentrations of H2CO3, H+ and HCO3-, we can assume that the equilibrium concentrations of these species are equal to their concentrations at the start of the reaction. Therefore, [H2CO3] = [H+] = [HCO3-] = 0.0004 mol/L.

5. Use the Ka expression to solve for [H+]: Ka1 = [H+][HCO3-] / [H2CO3] 4.45 x 10^-7 = [H+]^2 / 0.0004 [H+] = sqrt(4.45 x 10^-7 * 0.0004) [H+] = 1.33 x 10^-5 mol/L

6. Use the definition of pH to calculate the pH: pH = -log[H+] pH = -log(1.33 x 10^-5) pH = 4.88

Therefore, the pH of natural rainwater, given a CO2 concentration of 390 ppm at 25ºC and 1 atm, is approximately 4.88. This is slightly acidic, which is consistent with the fact that rainwater is naturally slightly acidic due to the presence of dissolved CO2.