Carbon dioxide dissolves in water to form carbonic acid, which is primarily dissolved CO2. Dissolved CO2 satisfies the equilibrium equation:
CO2 (g) <----> CO2 (aq) K=0.032
The acid dissociation constants listed in most standard reference texts for carbonic acid actually apply to dissolved CO2.
For a CO2 partial pressure of 4.4×10-4 atm in the atmosphere, what is the pH of water in equilibrium with the atmosphere?
To determine the pH of water in equilibrium with the atmosphere, we can use the equilibrium constant (K) and the concept of acid dissociation.
First, we need to understand that the concentration of carbonic acid in water can be calculated from the partial pressure of CO2 in the atmosphere using Henry's law. According to Henry's law, the concentration of a gas in a liquid is directly proportional to its partial pressure.
CO2 (g) <----> CO2 (aq)
Using Henry's law, we can calculate the concentration of dissolved CO2 by multiplying the CO2 partial pressure by a constant, which is determined experimentally. Let's assume this constant is represented by the symbol "H":
[CO2 (aq)] = H x (CO2 partial pressure)
Next, we can use the equilibrium constant (K) to determine the concentration of H+ ions and calculate the pH. The equilibrium equation for the ionization of dissolved CO2 is:
CO2 (aq) <----> H+ (aq) + HCO3- (aq)
According to the equilibrium equation, K = [H+][HCO3-]/[CO2 (aq)]
Given that K = 0.032, we can assume that the concentrations of H+ and HCO3- are x and x, respectively, while the concentration of CO2 (aq) will be the concentration of dissolved CO2 we calculated earlier.
Substituting the values into the equation, we get:
0.032 = x * x / [CO2 (aq)]
Now, we can substitute the concentration of dissolved CO2 (H x CO2 partial pressure) instead of [CO2 (aq)]. Let's call the concentration of dissolved CO2 as [CO2]:
0.032 = x * x / [CO2]
We can rearrange the equation to solve for x:
x^2 = 0.032 * [CO2]
x = sqrt(0.032 * [CO2])
Now, we know that pH is defined as the negative logarithm (base 10) of the H+ concentration:
pH = -log[H+]
Therefore, to calculate the pH, we need to calculate the H+ concentration. Since we assumed the concentration of H+ to be x:
[H+] = x
[H+] = sqrt(0.032 * [CO2])
Finally, we can substitute the concentration of dissolved CO2 using Henry's law:
[H+] = sqrt(0.032 * (H * CO2 partial pressure))
Now, you can calculate the pH by taking the negative logarithm of [H+]:
pH = -log(sqrt(0.032 * (H * CO2 partial pressure)))
Substituting the given CO2 partial pressure value of 4.4×10-4 atm, you can calculate the pH.