Due to increased CO2 in the atmosphere, the pH of rainwater is more acidic than in the previous century. Use the following data to calculate the pH of unpolluted rainwater at 25°C: vol% in air of CO2 = 0.033; solubility of CO2 in pure water at 25°C and 1 atm = 88 mL CO2 per 100 mL H2O; Ka1 of H2CO3 = 4.5 × 10–7.

Question

Due to increased CO2 in the atmosphere, the pH of rainwater is more acidic than in the previous century. Use the following data to calculate the pH of unpolluted rainwater at 25°C: vol% in air of CO2 = 0.033; solubility of CO2 in pure water at 25°C and 1 atm = 88 mL CO2 per 100 mL H2O; Ka1 of H2CO3 = 4.5 × 10–7.

Answer 1

To calculate the pH of unpolluted rainwater at 25°C, we need to consider the acidity caused by dissolved CO2 in the rainwater. The dissolved CO2 reacts with water to form carbonic acid (H2CO3), which is responsible for the acidity of rainwater.

The first step is to calculate the concentration of dissolved CO2 in the rainwater.

Given data:
- vol% in air of CO2 = 0.033
- solubility of CO2 in pure water at 25°C and 1 atm = 88 mL CO2 per 100 mL H2O

We can convert the vol% of CO2 in air to moles/Liter (Molarity) using the ideal gas law:
PV = nRT

Assuming the pressure (P) is 1 atm, the volume (V) is 0.033 * 22.414 L (using molar volume at 1 atm and 25°C), the temperature (T) is 25°C converted to Kelvin (298K), and the gas constant (R) is 0.0821 atm L/mol K, we can solve for n (moles of CO2).

n = (PV) / (RT)

Substituting the values, we get:
n = (1 atm * 0.033 * 22.414 L) / (0.0821 atm L/mol K * 298 K)

Now we can calculate the concentration of CO2 in moles/Liter (Molarity) using the solubility given:

Concentration of CO2 = (moles of CO2) / (volume of water) = (n) / (100 mL)

Substituting the values, we get:
Concentration of CO2 = (n) / (100 mL) = (n) / (0.1 L)

Next, we need to calculate the concentration of carbonic acid (H2CO3) formed from the dissolved CO2. The Ka1 value of H2CO3 provided is the acid dissociation constant for the first dissociation reaction of carbonic acid.

The equation for the first dissociation of carbonic acid is:
H2CO3 ⇌ H+ + HCO3-

Using the Ka expression:
Ka1 = [H+][HCO3-] / [H2CO3]

Assuming the concentration of carbonic acid (H2CO3) formed from dissolved CO2 is x, the concentration of H+ is x, and the concentration of HCO3- is x, we can write the equation:

Ka1 = (x)(x) / (x)

Since x represents the concentration of carbonic acid formed, Ka1 can be rewritten as:

Ka1 = x^2 / x = x

Now we can solve for x by substituting the Ka1 value:

x = Ka1 = 4.5 × 10^(-7) (Molarity of H+)

Finally, we can calculate the pH using the concentration of the H+ ion:

pH = -log[H+]

Substituting the value of [H+], we get:

pH = -log(4.5 × 10^(-7))

Calculating this expression will give us the pH of unpolluted rainwater at 25°C.