You perform a titration of $\ce{CH3COOH}$ with $\ce{NaOH}$. Let the original concentration of acetic acid be $\pu{0.2 M}$. The volumes of $\ce{CH3COOH}$ and $\ce{NaOH}$ are the same. Then the equivalence point will be reached when equivolume of $\pu{0.2 M}$ of $\ce{NaOH}$ has been added to the solution. At the equivalence point, the $\mathrm{pH}$ will be above 7. How does one calculate the exact $\mathrm{pH}$ value of the solution, which will be at the equilibrium point? The reactions we have are:
$$\ce{CH3COOH + OH- <=> CH3COO- + H2O} \tag1$$ ($\ce{Na^+}$ is a bystander or spectator ion, and therefore I ignored here).
The equilibrium constant for the given reaction is $K_1 = 1/K_b(\ce{CH3COO^-}) \gg 0$. We also have the following reaction:
For the reaction, $$\ce{CH3COO- + H3O+ <=> CH3COOH + H2O} \tag2$$, the equilibrium constant is $K_2 = 1/K_a(\ce{CH3COOH}) \gg 0$.
It is argued on other posts here that the first reaction "essentially" goes to completion and because $\ce{CH3COO-}$ later reacts with $\ce{H3O+}$ in the reaction $(2)$, the $\mathrm{pH}$ will be above 7. However, this motivation seems flawed to me. When the second reaction occurs, that will decrease the concentration of $\ce{CH3COO-}$, which will trigger reaction $(1)$ to move to the right. This will decrease the concentration of $\ce{OH^-$ ions. I know that the rate at which the concentration of $OH-}$ decreases in reaction $(1)$ and the rate at which the concentration of $\ce{H3O+}$ decreases in reaction $(2)$ are not equal due to the different equilibrium constants for these two reactions. However, I don't understand how to calculate this $\mathrm{pH}$ using the above logic.
Could anyone show how to calculate the $\mathrm{pH}$ that this titration will have at the equivalence point using logic above? Thanks!