To estimate the pH of rain on that day, we need to follow a series of logical steps that involve understanding the concentration of sulfur dioxide (SO2) in the atmosphere, its solubility in water, and how it forms sulfurous acid (H2SO3) when dissolved. Let's break this down step by step.
Step 1: Convert SO2 Concentration from ppm to Molarity
The concentration of SO2 in the atmosphere is given as 10 ppm (parts per million). To convert this to molarity (M), we can use the following relationship:
- 1 ppm = 1 mg/L
- Molar mass of SO2 = 64.07 g/mol
First, we convert 10 ppm to mg/L:
10 ppm = 10 mg/L
Now, convert mg/L to moles per liter (M):
10 mg/L = 10 mg/L × (1 g/1000 mg) × (1 mol/64.07 g) = 0.000156 mol/L
Step 2: Calculate the Concentration of H2SO3
When SO2 dissolves in water, it forms sulfurous acid (H2SO3). The solubility of SO2 is given as 1.3653 moles/L at 298K, which means that at saturation, the concentration of H2SO3 will be equal to the concentration of dissolved SO2. However, since we have a lower concentration of SO2 (0.000156 mol/L), we can assume that all of this will convert to H2SO3.
Step 3: Determine the Concentration of H+ Ions
To find the pH, we need to determine the concentration of hydrogen ions (H+) produced from H2SO3. The dissociation of H2SO3 can be represented as follows:
H2SO3 ⇌ H+ + HSO3-
The dissociation constant (Ka) for this reaction can be calculated from the given pKa:
pKa = 1.92, therefore Ka = 10^(-1.92) ≈ 0.0121
Step 4: Apply the Equilibrium Expression
Using the equilibrium expression for the dissociation of H2SO3:
Ka = [H+][HSO3-] / [H2SO3]
Assuming that x is the concentration of H+ ions produced, we can set up the equation:
0.0121 = (x)(x) / (0.000156 - x)
Since x will be very small compared to 0.000156, we can simplify this to:
0.0121 ≈ (x^2) / (0.000156)
Solving for x gives:
x^2 = 0.0121 × 0.000156
x^2 ≈ 1.89 × 10^-6
x ≈ 0.001375
Step 5: Calculate the pH
Now that we have the concentration of H+ ions, we can calculate the pH:
pH = -log[H+] = -log(0.001375) ≈ 2.86
Final Result
Therefore, the estimated pH of rain on that day, given the concentration of SO2 and its solubility, is approximately 2.86. This indicates that the rain would be quite acidic, which is typical in urban areas with higher levels of air pollution.
