The \(\mathrm{pH}\) of a particular raindrop is 5.6. (a) Assuming the major species in the raindrop are $\mathrm{H}_{2} \mathrm{CO}_{3}(a q), \mathrm{HCO}_{3}^{-}(a q),\( and \)\mathrm{CO}_{3}^{2-}(a q),$ calculate the concentrations of these species in the raindrop, assuming the total carbonate concentration is \(1.0 \times 10^{-5} \mathrm{M}\). The appropriate \(K_{a}\) values are given in Table 16.3. (b) What experiments could you do to test the hypothesis that the rain also contains sulfur-containing species that contribute to its pH? Assume you have a large sample of rain to test.

We are given the following information: - pH of the raindrop = 5.6 - Total carbonate concentration = \(1.0 \times 10^{-5} M\) - Equilibrium constants (K_a) for H2CO3 and HCO3- (Table 16.3) We need to find the concentrations of H2CO3, HCO3-, and CO3^2-. Write the equilibrium equations for the relevant reactions: 1. \(H_2CO_3 \leftrightarrows H^+ + HCO_3^-\) with equilibrium constant \(K_{a1}\) 2. \(HCO_3^- \leftrightarrows H^+ + CO_3^{2-}\) with equilibrium constant \(K_{a2}\)

We have the pH value, so we can find the concentration of H+ ions: \(pH = -\log[H^+]\) Solve for [H+]: \([H^+] = 10^{-5.6} M\)

Write the equilibrium expressions for the two reactions: \(K_{a1} = \frac{[H^+][HCO_3^-]}{[H_2CO_3]}\) \(K_{a2} = \frac{[H^+][CO_3^{2-}]}{[HCO_3^-]}\) From Table 16.3, we have \(K_{a1} = 4.45 \times 10^{-7}\) and \(K_{a2} = 4.69 \times 10^{-11}\). Assume that the concentration of H2CO3 is much greater than the concentration of CO3^2-, so: Total carbonate concentration ≈ [H2CO3] + [HCO3^-]

Using the assumed relationship: \(1.0 \times 10^{-5} M = [H_2CO_3] + [HCO_3^-]\) Now, we have equations for K_a1 and K_a2 in terms of the concentrations. We can substitute [H+] from Step 2 and solve the equations simultaneously to find the concentrations of the three species: 1. \(4.45 \times 10^{-7} = \frac{10^{-5.6} [HCO_3^-]}{[H_2CO_3]}\) 2. \(4.69 \times 10^{-11} = \frac{10^{-5.6} [CO_3^{2-}]}{[HCO_3^-]}\) Solving these equations simultaneously, we obtain: [H2CO3] ≈ \(9.1 \times 10^{-6} M\) [HCO3-] ≈ \(9.0 \times 10^{-6} M\) [CO3^2-] ≈ \(1.0 \times 10^{-10} M\)

To test for the presence of sulfur-containing species in the rain, such as sulfuric acid (H2SO4) or sulfurous acid (H2SO3), some possible experiments include: 1. Conduct a quantitative analysis using Ion Chromatography (IC) to detect and measure the concentrations of sulfate (SO4^2-) and sulfite (SO3^2-) ions in the rain sample. 2. Perform a qualitative test for sulfate ions using a barium chloride solution. Add a few drops of barium chloride solution to the rain sample, and observe if a white precipitate of barium sulfate (BaSO4) forms, indicating the presence of sulfate ions. 3. Carry out a similar qualitative test for sulfite ions using potassium permanganate solution. When added to a solution containing sulfite ions, the purple color of potassium permanganate solution will fade due to reduction, indicating the presence of sulfite ions. By performing these experiments, we can determine the presence of sulfur-containing species in the raindrop that may contribute to its pH.