To calculate the concentration of (Co3)2- in the solution, we need to consider the reactions related to the dissolution of Co2 and the subsequent hydration and dissociation of H2CO3.
1. First, let's write the balanced equation for the dissolution of Co2 in water:
CO2 + H2O ⇌ H2CO3
According to the problem, we dissolved 1 mole of Co2 in 1 L of water, so the initial concentration of Co2 is 1 M.
2. Next, we need to consider the hydration equilibrium of H2CO3, which is an important step in the overall process:
H2CO3 + H2O ⇌ H3O+ + HCO3-
The hydration equilibrium constant (Kh) of H2CO3 is given as 1.70x10^-3.
3. It is also necessary to consider the dissociation of H2CO3 into (Co3)2- ions:
2HCO3- ⇌ H3O+ + (Co3)2-
The dissociation constants (Ka1 and Ka2) for H2CO3 are given as 2.5x10^-4 and 5.01x10^-11, respectively.
Now, let's calculate the concentration of (Co3)2- step-by-step.
Step 1: Calculate the equilibrium concentration of H2CO3 using the hydration constant Kh:
Kh = [H3O+][HCO3-] / [H2CO3]
Let's assume the concentration of H2CO3 at equilibrium is x.
Kh = [H3O+][HCO3-] / x
The concentration of water (H2O) is assumed to be constant, so we can ignore it.
Therefore, Kh = [H3O+][HCO3-] / x
Step 2: Calculate the concentration of (Co3)2- ions using the dissociation constants Ka1 and Ka2:
Ka1 = [H3O+][HCO3-] / [H2CO3]
Ka2 = [H3O+][(Co3)2-] / [HCO3-]
Let's assume the concentration of (Co3)2- ions at equilibrium is y.
Ka2 = [H3O+][y] / [HCO3-]
Rearranging the equation above, we get:
[y] = (Ka2 * [HCO3-]) / [H3O+]
Step 3: Finally, we need to express the concentration of (Co3)2- ions in terms of H2CO3:
Since H2CO3 dissociates into 2HCO3-, the concentration of [HCO3-] is 2x.
[y] = (Ka2 * [HCO3-]) / [H3O+]
= (Ka2 * 2x) / (x)
Simplifying the equation above, we get:
[y] = 2 * Ka2
Therefore, the concentration of (Co3)2- in the solution is 2 * Ka2. You can substitute the given value of Ka2 (5.01x10^-11) into the equation to find the final answer.