I have a question regarding the titration curve. When the ph is equal pKa that mean there are equal amount of conjugate acid to conjugate base. When a weak acid dissociates for example

H3Po4 H+ H2PO4-
My problem: I don’t understand how the ph rises after the halfway mark ( when ph = pka ) we are producing equal amounts of conjugate base and Hydrogen ions simultaneously
Also, Why is the conjugate base more in concentration after the halfway mark?

H3PO4 ==> H^+ + H2PO4^-

At the half-way point, you're right.
(base) = (acid)
But for the remainder of your question you may be confusing H^+ with the other parts. You are titrating H3PO4 with a base, say NaOH, so
H3PO4 + OH^- ==> H2O + H2PO4^-
pH = pKa + log [(H2PO4^-)/(H3PO4)].
After the half-way point, H2PO4^- is increasing and H3PO4 is decreasing. The pH increases for that reason. There is less acid and more base. I don't see that any H^+ is being produced. In fact, H^+ is being neutralized to H2O.
I hope I have interpreted your question properly.
A couple of days ago I helped you with a problem and I suggested you might want to get a second opinion. I have forgotten the problem now(I think it was the carboxylic acid pKa + a pk2) and the question was to find pK2.) but I'm curious as to the outcome. I would appreciate a summary of that work and the outcome.

To understand why the pH rises after the halfway mark in a titration curve, we need to consider the reaction and equilibrium that take place during the titration.

In the case of the weak acid H3PO4 dissociating into H+ and H2PO4-, the equilibrium can be represented as:

H3PO4 ↔ H+ + H2PO4-

At the start of the titration, before any base is added, the solution contains only the weak acid H3PO4. As you add the base (e.g., NaOH), it reacts with the H3PO4 to form water and the conjugate base (H2PO4-):

NaOH + H3PO4 → H2O + NaH2PO4

During this initial stage, the pH of the solution remains relatively constant because the concentration of H3PO4 is still much higher than that of H2PO4-. This is before the halfway mark on the titration curve.

As you continue to add the base, the amount of H2PO4- increases, and the concentration of H3PO4 decreases. At the halfway mark, the concentration of H3PO4 equals that of H2PO4-, and the pH equals the pKa of the weak acid. So, at this point, you have equal amounts of the conjugate acid (H3PO4) and the conjugate base (H2PO4-).

Now, beyond the halfway mark, when the titrant (base) is in excess, there is a surplus of OH- ions from the base. These excess OH- ions react with the remaining H2PO4- to form HPO4²-, which is a stronger base than H2PO4-:

OH- + H2PO4- → HPO4²- + H2O

This reaction results in the production of hydroxide ions (OH-) and the consumption of H2PO4-, causing a decrease in the overall acidity of the solution. Consequently, as the OH- ions neutrality the solution, the pH rises.

Therefore, after the halfway mark, the pH rises because the additional base reacts with the remaining weak acid's conjugate base to produce more hydroxide ions which leads to a decrease in acidity and an increase in pH.

As a result, the conjugate base (H2PO4-) is more in concentration after the halfway mark because the initial weak acid (H3PO4) has been consumed, and the excess base reacts with the remaining H2PO4- to form HPO4²-. This shift towards the conjugate base side further increases the concentration of H2PO4- as the titration continues.