Carbon dioxide dissolves in water to form carbonic acid, which is primarily dissolved CO2. Dissolved CO2 satisfies the equilibrium equation.

The acid dissociation constants listed in most standard reference texts for carbonic acid actually apply to dissolved CO2. K=0.032 M/atm

For a CO2 partial pressure of 2.4×10-4 atm in the atmosphere, what is the pH of water in equilibrium with the atmosphere?

Since carbonic acid is primarily dissolved CO2, the concentration of H2CO3 can be taken as equal to that of dissolved CO2,

[H2CO3]=[CO2aq]
The equilibrium equation for the dissolution of gaseous CO2 can be used to calculate the [CO2(aq)] and, hence, the [H2CO3]. The [H2CO3] will then be used to calculate the pH. Dissolved CO2 satisfies the equilibrium equation
pH=5.609

can you show step by step how you got that pH?

To find the pH of water in equilibrium with the atmosphere, we need to use the equilibrium equation for carbonic acid. The equilibrium equation for the dissociation of carbonic acid can be written as follows:

CO2 + H2O ⇌ H2CO3

The dissociation constant (K) for this equilibrium equation is given as 0.032 M/atm.

Given that the partial pressure of CO2 in the atmosphere is 2.4×10-4 atm, we can use this information to find the concentration (C) of H2CO3 in the water.

First, we need to convert the partial pressure to the concentration of dissolved CO2 using Henry's Law, which states that the concentration of a gas dissolved in a liquid is directly proportional to its partial pressure. The equation for Henry's Law is as follows:

C = K * P

Where C is the concentration, K is the Henry's Law constant, and P is the partial pressure.

Plugging in the values, we have:

C = (0.032 M/atm) * (2.4×10-4 atm)
C = 7.68×10-6 M

Now that we have the concentration of H2CO3, we can use it to calculate the pH. Carbonic acid (H2CO3) when dissolved in water, dissociates into a hydrogen ion (H+) and a bicarbonate ion (HCO3-). The equation for this dissociation is as follows:

H2CO3 ⇌ H+ + HCO3-

Since H2CO3 is a weak acid, we can assume that the concentration of H+ from the dissociation of H2CO3 is approximately equal to the concentration of H2CO3 itself.

Therefore, the concentration of H+ is 7.68×10-6 M.

Using the equation for pH, which is defined as the negative logarithm of the concentration of H+:

pH = -log[H+]

Plugging in the value, we have:

pH = -log(7.68×10-6)
pH ≈ 5.11

Therefore, the pH of water in equilibrium with the atmosphere at a CO2 partial pressure of 2.4×10-4 atm is approximately 5.11.