Final answer:
The pH of the rainwater with a CO₂ concentration of 700 ppm and a partial pressure of 10⁻³² atm is approximately 7.23, calculated by determining the concentration of dissolved CO₂, the formation of carbonic acid, and using the dissociation constant. The alkalinity of rainwater in mg/L as CaCO₃ cannot be calculated accurately without additional information.
Step-by-step explanation:
To calculate the pH of rainwater with a current CO₂ concentration of 700 ppm (partial pressure 10⁻³² atm), we can use the fact that CO₂ when dissolved in water forms carbonic acid (H₂CO₃), which further dissociates into bicarbonate (HCO₃⁻) and hydronium ions (H₃O⁺). The first step is to calculate the concentration of dissolved CO₂ in water using Henry's law (Kₓ = [CO₂] / P₂), in this case: [CO₂] = Kₓ * P₂ = 31.6 atm.M¹ * 10⁻³² atm = 2.0 x 10⁻µ M. Because only a fraction of this CO₂ forms carbonic acid, we use the equilibrium constant for the formation of carbonic acid (Kₘ) to find its concentration: [H₂CO₃] = Kₘ * [CO₂] = 1.58x10⁻³ * 2.0 x 10⁻µ M = 3.16 x 10⁻¸ M.
Once we have the concentration of carbonic acid, we can use the first dissociation constant for carbonic acid (K1) to find the concentration of hydronium ions: [H₃O⁺] = √(K1 * [H₂CO₃]) = √((4.45x10⁻⁷ M) * (3.16 x 10⁻¸ M)) ≈ 5.95 x 10⁻¸ M. Then, we calculate the pH of the rainwater: pH = -log[H₃O⁺] = -log(5.95 x 10⁻¸) ≈ 7.23.
To calculate the alkalinity of the rainwater as mg/L as CaCO₃, we would need the total concentration of all species that can neutralize acid, which primarily includes bicarbonate and carbonate species. This calculation is more complex as it involves the equilibrium between carbonic acid, bicarbonate, and carbonate, as well as the second dissociation constant (K2) of carbonic acid. Hence, without additional information, we cannot accurately calculate the alkalinity in the given units. However, in principle, the concentration of bicarbonate ions could be calculated, and the equivalent weight of CaCO₃ could be used to convert this concentration into the desired units.