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 \(1.0 \times 10^{-5} M .\) 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 \(\mathrm{pH}\) ? Assume you have a large sample of rain to test.

The total carbonate concentration in the raindrop is the sum of the concentrations of each form of carbonate. That is: Total Carbonate = [H2CO3] + [HCO3-] + [CO3^2-] = \(1.0 \times 10^{-3} M\)

The total positive charge should be equal to the total negative charge in the raindrop. We also have to consider the main source of hydrogen ion (\(H^{+}\)) and hydroxide ion (\(OH^{-}\)) concentrations when writing this equation. So, the charge balance equation can be written as: \[ [H^+] = [HCO_3^-] + 2[CO_3^{2-}] + [OH^-] \]

We are given two equilibrium constants for the dissociation of carbonic acid: \(K_{a1} = \frac{[H^+][HCO_3^-]}{[H_2CO_3]}\) \(K_{a2} = \frac{[H^+][CO_3^{2-}]}{[HCO_3^-]}\)

The pH of the raindrop is 5.6, so we can determine the hydrogen ion concentration as follows: \[ [H^+] = 10^{-pH} = 10^{-5.6} \]

We can find the hydroxide ion concentration from the ion product of water: \[ K_w = [H^+][OH^-] \] Where \(K_w = 10^{-14}\), so \[ [OH^-] = \frac{10^{-14}}{[H^+]} \]

With all the needed equations, we can now solve the system of equations. We can substitute equations from Step 1, 3, and 4 into the charge balance equation (Step 2). We can then solve for [HCO3-] and [CO3^2-]. After determining the concentration of these species, we can find [H2CO3] using the mass balance equation. Part (b):

The hypothesis is that the raindrop contains sulfur-containing species that contribute to its pH. We can perform the following experiments: 1. Perform a filtration test: A simple filtration test may help in removing any solid-form sulfur compounds like sulfates. Measure the pH after filtration and compare it with the initial pH. 2. Conduct chemical tests to detect the presence of sulfurous compounds: Colorimetric, ion-selective electrode, or chromatography methods can detect the presence of sulfur-containing species, such as sulfates or sulfites, in the raindrop sample. 3. Add a sulfur scavenger: Adding a chemical that reacts with sulfur-containing species and removes them can help determine if the pH changes after treating the sample with the scavenger. If the pH changes, this indicates that sulfur-containing species contribute to the initial pH. These experiments can help in verifying the presence of sulfur-containing species in raindrops and determining their contribution to the pH values.