Sulfur dioxide is quite soluble in water: SO2(g) + H2O(l) ⇌ H2SO3(aq), K = 1.33. The H2SO3 produced is a weak diprotic acid (Ka1 = 1.5 * 10^-2; Ka2 = 6.3 * 10^-8). Calculate the pH and the concentrations of H2SO3, HSO3-, and SO3^2- in a solution prepared by continuously bubbling SO2 at a pressure of 1.00 atm into pure water.

Verified step by step guidance

1. Step 1: Use Henry's Law to determine the concentration of dissolved SO2 in water. Henry's Law states that the concentration of a gas in a liquid is proportional to the partial pressure of the gas above the liquid. The formula is C = kH * P, where C is the concentration, kH is the Henry's Law constant for SO2, and P is the pressure of SO2.
2. Step 2: Recognize that the dissolved SO2 reacts with water to form H2SO3 according to the equilibrium: SO2(g) + H2O(l) ⇌ H2SO3(aq). Use the equilibrium constant K = 1.33 to find the concentration of H2SO3 at equilibrium.
3. Step 3: Consider the dissociation of H2SO3 in water. Since H2SO3 is a diprotic acid, it dissociates in two steps: H2SO3 ⇌ H+ + HSO3- (with Ka1) and HSO3- ⇌ H+ + SO3^2- (with Ka2). Use the given Ka1 and Ka2 values to set up equilibrium expressions for each dissociation step.
4. Step 4: Calculate the concentration of H+ ions from the first dissociation step using the expression [H+] = sqrt(Ka1 * [H2SO3]). This will help in determining the pH of the solution.
5. Step 5: Use the concentrations from the first dissociation to find the concentration of HSO3- and then use the second dissociation equilibrium to find the concentration of SO3^2-. Use the expressions [HSO3-] = [H+] and [SO3^2-] = Ka2 * [HSO3-] / [H+].

Key Concepts

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. In this case, K = 1.33 indicates that at equilibrium, the concentration of H2SO3 is favored over the reactants. Understanding K helps predict how changes in conditions affect the position of equilibrium and the concentrations of species in solution.

Weak Acids and Their Dissociation

Weak acids, like H2SO3, do not fully dissociate in solution, which means they establish an equilibrium between the undissociated acid and its ions. The dissociation constants (Ka1 and Ka2) provide insight into the strength of the acid and the extent of dissociation. For H2SO3, Ka1 = 1.5 * 10^-2 indicates that the first dissociation is relatively strong, while Ka2 = 6.3 * 10^-8 shows the second dissociation is much weaker.

pH Calculation

pH is a measure of the hydrogen ion concentration in a solution, calculated using the formula pH = -log[H+]. In solutions of weak acids, the pH can be determined from the concentrations of the acid and its dissociated ions. For this problem, calculating the pH involves determining the equilibrium concentrations of H2SO3, HSO3-, and SO3^2- and using these to find the concentration of H+ ions.