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.

To calculate the pH of unpolluted rainwater at 25°C, we can use the reaction between dissolved CO2 and water to form carbonic acid (H2CO3). Carbonic acid is a weak acid and can be represented by the following equation:

CO2 + H2O ⇌ H2CO3

To calculate the pH, we need to determine the concentration of H2CO3 in the rainwater. First, let's calculate the concentration of dissolved CO2 in the rainwater.

1. Calculate the concentration of CO2 in pure water at 25°C and 1 atm:
From the given data, we know that the solubility of CO2 in pure water at 25°C and 1 atm is 88 mL CO2 per 100 mL H2O. Since mL is a volumetric unit, we need to convert it to moles per liter (M):

88 mL CO2/100 mL H2O = 0.88 moles CO2/1 liter H2O

2. Calculate the concentration of H2CO3:
Since the ratio between CO2 and H2CO3 is 1:1, the concentration of H2CO3 will be the same as the concentration of CO2:

0.88 moles H2CO3/1 liter H2O

3. Convert the concentration to molarity (M):
The concentration given above is in moles per liter of water. Therefore, the molarity (M) of H2CO3 will be the same:

0.88 M H2CO3

4. Calculate the pH using the Ka1 of H2CO3:
The Ka1 of H2CO3 is given as 4.5 × 10–7. The relationship between the H2CO3, H+, and HCO3- concentrations is described by the equilibrium constant expression:

Ka1 = [H+][HCO3-] / [H2CO3]

Since H2CO3 is a weak acid, it largely dissociates into H+ and HCO3-. Therefore, we can neglect the concentration change of H2CO3 compared to HCO3- and H+.

Ka1 = [H+]^2 / [H2CO3]

We can rearrange this equation to solve for [H+]:

[H+]^2 = Ka1 * [H2CO3]

[H+] = sqrt(Ka1 * [H2CO3])

Substituting the values we calculated earlier:

[H+] = sqrt(4.5 × 10–7 * 0.88)

Finally, calculate the pH using the [H+] concentration:

pH = -log10([H+])

You can use a scientific calculator or any software/app that allows you to perform these calculations to find the final pH value.

To calculate the pH of unpolluted rainwater at 25°C, we can use the following steps:

1. Calculate the concentration of dissolved CO2 in unpolluted rainwater:
- The solubility of CO2 in pure water at 25°C and 1 atm is given as 88 mL CO2 per 100 mL H2O.
- Convert the volume percent of CO2 in air to a concentration by multiplying it by the solubility factor:
- Concentration of CO2 = 0.033 * 88/100 = 0.02904 mol/L

2. Calculate the concentration of carbonic acid (H2CO3) formed by the dissolved CO2:
- Carbonic acid (H2CO3) is formed when CO2 dissolves in water according to the following reaction:
CO2(g) + H2O(l) ⇌ H2CO3(aq)
- Since the concentration of CO2 in rainwater is the same as the concentration of H2CO3, we can assume them to be equal:
- Concentration of H2CO3 = 0.02904 mol/L

3. Calculate the concentration of hydrogen ions (H+) from the dissociation of carbonic acid (H2CO3):
- The equilibrium reaction for the dissociation of carbonic acid is:
H2CO3(aq) ⇌ H+(aq) + HCO3-(aq)
- The equilibrium constant (Ka1) for this reaction is given as 4.5 × 10^(-7).
- Let x be the concentration of H+ in mol/L at equilibrium.
- Since H2CO3 dissociates to form one H+ ion, the concentration of HCO3- will also be equal to x:
- [H+] = [HCO3-] = x

Using the equilibrium constant expression for the dissociation of carbonic acid:
Ka1 = [H+][HCO3-] / [H2CO3]
4.5 × 10^(-7) = x * x / 0.02904

4. Solve the equation for x to find the concentration of H+ ions:
- Rearrange the equation:
x^2 = 4.5 × 10^(-7) * 0.02904
x^2 = 1.306 × 10^(-8)
x ≈ 1.144 × 10^(-4) mol/L

5. Calculate the pH of unpolluted rainwater:
- pH is defined as the negative logarithm (base 10) of the concentration of H+ ions:
- pH = -log[H+]
- pH = -log(1.144 × 10^(-4))
- pH ≈ 3.94

Therefore, the pH of unpolluted rainwater at 25°C is approximately 3.94.