Acid rain takes place dur to combination of acidic oxides with water and it is an envirronmental concern all over the world. Assuming rain water is uncontaminated with `HNO_(3)` or `H_(2)SO_(4)` and is in equilibrium with `1.25 xx 10^(-4)` atm `CO_(2)`. The Henry's law constant `(K_(H))` is `1.25 xx 10^(6) "torr". K_(a_(1))` of `H_(2)CO_(3) = 4.3 xx 10^(-7)`
Given : `K_(f)CuCI^(Theta) = 1.0 (K_(f)` is formation constant of `CuCI^(o+))`
If `SO_(2)` content is the atomsphere is `0.64 "ppm"` by volume, `pH` of rain water is (assume `100%` ionisation of acid rain as monobasic acid).

Options

A. `4.0`
B. `5.0`
C. `6.0`
D. `7.0`

Explanation

To solve the problem of calculating the pH of rainwater due to the presence of sulfur dioxide (SO₂) in the atmosphere, we will follow these steps:

### Step 1: Understand the Reaction
When sulfur dioxide (SO₂) dissolves in water, it forms sulfurous acid (H₂SO₃):
\[ \text{SO}_2(g) + \text{H}_2\text{O}(l) \rightleftharpoons \text{H}_2\text{SO}_3(aq) \]

### Step 2: Calculate the Concentration of SO₂
Given that the concentration of SO₂ in the atmosphere is 0.64 ppm by volume, we can convert this to grams:
- 0.64 ppm means 0.64 grams of SO₂ in 1,000,000 mL of air.

Next, we need to convert grams to moles using the molar mass of SO₂ (approximately 64 g/mol):
\[ \text{Moles of SO}_2 = \frac{0.64 \text{ g}}{64 \text{ g/mol}} = 0.01 \text{ mol} \]

### Step 3: Calculate the Concentration in Molarity
To find the concentration in molarity (M), we need to convert the volume from mL to L:
\[ \text{Volume in L} = \frac{1,000,000 \text{ mL}}{1000} = 1000 \text{ L} \]
Now, calculate the concentration:
\[ \text{Concentration of SO}_2 = \frac{0.01 \text{ mol}}{1000 \text{ L}} = 1.0 \times 10^{-5} \text{ M} \]

### Step 4: Determine the Concentration of H⁺ Ions
Since we assume 100% ionization of H₂SO₃ as a monobasic acid, it will dissociate to produce one H⁺ ion per molecule:
\[ \text{H}_2\text{SO}_3 \rightleftharpoons \text{H}^+ + \text{HSO}_3^- \]
Thus, the concentration of H⁺ ions will be equal to the concentration of SO₂:
\[ [\text{H}^+] = 1.0 \times 10^{-5} \text{ M} \]

### Step 5: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
Substituting the value of [H⁺]:
\[ \text{pH} = -\log(1.0 \times 10^{-5}) = 5 \]

### Conclusion
The pH of the rainwater due to the SO₂ content in the atmosphere is **5**.