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 6.1×10-4 atm in the atmosphere, what is the pH of water in equilibrium with the atmosphere?
i've literally tried this 9 times and got it wrong everytime, please help!
To find the pH of water in equilibrium with the atmosphere, we need to calculate the concentration of H+ ions using the equilibrium constant K and the partial pressure of CO2.
The equilibrium equation given is:
CO2(g) ⇌ CO2(aq)
The equilibrium constant K is given as 0.032. This equilibrium equation can be related to the following chemical reaction:
CO2(aq) + H2O ⇌ H2CO3(aq)
The dissociation constant K for carbonic acid is related to the equilibrium constant K as follows:
K = [H2CO3] / [CO2(aq)]
We can assume that the concentration of dissolved carbon dioxide ([CO2(aq)]) is the same as the partial pressure of CO2 (6.1×10-4 atm), keeping in mind that they are not exactly the same but are related due to Henry's Law.
Let x be the concentration of H2CO3(aq) and [H+] be the concentration of H+ ions. The equilibrium expression for the dissociation constant K of carbonic acid can be written as:
0.032 = x /[CO2(aq)] * [H+]
Since we are looking for the pH, we can assume that the concentration of H+ ions is equal to x.
0.032 = [CO2(aq)] * [H+]
[CO2(aq)] = 6.1×10-4 atm
Substituting the values:
0.032 = (6.1×10-4 atm) * [H+]
[H+] = 0.032 / (6.1×10-4 atm)
[H+] ≈ 52.46 M
Now, we can use the concentration of H+ ions to find the pH using the equation:
pH = -log[H+]
pH = -log(52.46)
pH ≈ -1.72
Therefore, the pH of water in equilibrium with the atmosphere, for a CO2 partial pressure of 6.1×10-4 atm, is approximately -1.72.
To solve this problem, we need to use the concept of acid dissociation equilibrium and the expression for pH.
First, let's understand the given equilibrium equation:
CO2(g) ⇌ CO2(aq)
This equation represents the conversion of gaseous carbon dioxide (CO2) into dissolved carbon dioxide (CO2(aq)). The value of the equilibrium constant (K) is given as 0.032.
Next, let's consider the reaction of carbonic acid with water:
CO2(aq) + H2O ⇌ H2CO3(aq)
Here, CO2(aq) reacts with water (H2O) to form carbonic acid (H2CO3(aq)). Note that H2CO3(aq) dissociates into H+ and HCO3- ions, but this dissociation is negligible compared to the reaction with water.
Now, we can write the equilibrium constant expression for the formation of carbonic acid:
K = [H2CO3(aq)] / [CO2(aq)]
However, we know that carbonic acid is primarily in the dissolved CO2 form, so we can rewrite the expression as:
K = [CO2(aq)] / [CO2(g)]
Since we're given the value of K as 0.032, we can substitute this into the equation:
0.032 = [CO2(aq)] / [CO2(g)]
Now, let's solve for [CO2(aq)]:
[CO2(aq)] = 0.032 × [CO2(g)]
The problem states that the CO2 partial pressure in the atmosphere is 6.1×10-4 atm. Therefore:
[CO2(aq)] = 0.032 × (6.1×10-4)
Now, we have the concentration of dissolved CO2, which we can use to calculate the pH of water in equilibrium with the atmosphere.
To proceed, we need to know the relationship between CO2(aq) concentration and the concentration of H+ ions. For carbonic acid, the pH is related to [H+] as follows:
pH = –log[H+]
But in this case, the concentration of H+ is identical to the concentration of dissolved CO2: [H+] = [CO2(aq)].
Hence, the pH of water in equilibrium with the atmosphere can be calculated as:
pH = –log[CO2(aq)]
Now, substituting the value of [CO2(aq)] into this equation will give us the final answer.
Please proceed with this calculation, and if you encounter any difficulties or if you need further assistance, feel free to ask!