u/Icy_Pattern_3363

I have been struggling with the standard textbook explanations for the conductometric titration of a weak acid (e.g., CH3COOH) with a strong base (e.g., NaOH). To help me visualize the process, I developed a mental model based on “competing vectors” and “converging progressions.”

I’ve discussed this with an AI, which found the logic sound, but I want to verify with the community if this physical intuition holds up or if I am oversimplifying the equilibrium dynamics.

Here I use vectors to explain equilibrium shifts and H+, OH-, and CH3COO- to show every step of the process. I also take a finite amount of reactant into consideration.

The reactions involved:

1. CH3COOH ⇌ H+ + CH3COO-
2. NaOH → Na+ + OH-
3. H+ + OH- → H2O
4. CH3COOH + NaOH → CH3COONa + H2O
5. CH3COONa → CH3COO- + Na+

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Phase 1: The Initial Dip

The initial dip in the graph is due to the H+ getting used and forming water with OH-, while the salt is also breaking, but H+ still contributes more to conductance due to its high mobility, so the graph dips.

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Phase 2: The Rising Curve

Now when NaOH is being added to CH3COOH, it forms CH3COONa, which reduces the amount of free H+ and disrupts the equilibrium:

CH3COOH ⇌ H+ + CH3COO-

This moves the equilibrium forward.

But then the salt breaks:

CH3COONa → CH3COO- + Na+

and it increases the CH3COO- concentration.

Now H+ is not really present in large amount because it is continuously reacting with OH-, so though the equilibrium now shifts backward due to increased acetate ion concentration, it only shifts slightly backward due to H+ not being included much in this process.

Now as reactant just got consumed by NaOH, the concentration of CH3COOH decreases, increasing degree of dissociation (α), so more CH3COO- gets produced and a new equilibrium is established.

But then just like before, more NaOH comes and disrupts it again, causing equilibrium to move forward, but then salt breaking causes a slight push back, resulting in a net slight forward shift.

Now as more CH3COO- was produced, the push back also increases more.

**So if we think of it like vectors:**

* increasing effect = Vector A * decreasing effect = Vector B * net increase = Vector A - Vector B

and this keeps happening repeatedly until they hit convergence where A = B and reactant is over.

**Example:**

S = 1 + 1/4 + 1/16 + 1/64 + ...

This hits a convergence somewhere, so I basically modeled the equilibrium with vectors and a geometric progression.

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Phase 3: Post-Equivalence

After CH3COOH is finished and NaOH is still being added, the graph increases sharply as excess NaOH is being added.

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My question

Is this “vector + convergence” interpretation physically meaningful as an intuition for equilibrium shifts during conductometric titration, or whether it fundamentally misrepresents the actual equilibrium behavior?