[seojunpark]

Hey chemists I'm trying to establish a conceptual relationship about acid base buffers for my calc bc final project. So for my project, I had an inspiration from the fact that titration curves get steeper the stronger the buffers are, and that the area under the curve changes so there is somehow an inverse relationship between buffer strength and the area under the curve.

However, I've found struggles conceptually on how to conduct the experiment because there isn't really such a thing like a buffer constant associated with each acid base buffer combination. So even if I get the area under the curve for different titration processes, I couldn't really relate them.

I've also found difficulties in setting up the initial conditions for different acid base buffers that would make them suitable for comparison. Perhaps a constant concentration of conjugate acid/base whatever throughout the buffer combinations?

I'm really intrigued about the concept of incorporating calculus to find relationships in chemistry, but at the same time I'm really perplexed. Is my proposed experiment practical? Or does it even make sense in the first place?

[Borek]

the fact that titration curves get steeper the stronger the buffers are

Not sure what you mean, strong buffer keeps the pH changes smaller, making the titration curve flat.

The only place where the titration curve gets steep is at the inflection point, but there we are far from the buffering range. And I don't think even there pH change is related to the buffer "strength" at pH where it will be typically used - pH change at inflection point is the highest for strong acids, while buffering capacity is the highest for weak acids.

[seojunpark]

Yea, I thought that I could somehow compare different buffer combinations at the buffer region, getting the area under the curve from 0 titrant added to equivalence point. Stronger buffers will be flatter thus will give less area, vice versa.

[Borek]

Stronger buffers will be flatter thus will give less area

So the first step is to precisely define what you mean by a "stronger" buffer. Not an obvious task. If your plan is to integrate over whole range of pHs during titration the answer can be useless, as the best buffer strength I am aware of, buffer capacity, is a function of pH:

https://www.chembuddy.com/pH-calculation-buffer-capacity

Say you get some (same, or different) result when integrating acetic acid and glycolic acid titration curves - what does such number tell about which buffer is better at pH 5 (which is how buffers are used)?

But to even try to integrate (which can produce some interesting results) you need a way to calculate titration curve (as in pH(V)) to integrate it. Not an easy and obvious problem, from what I remember it is actually easier to go other way around, and calculate V from pH.

Compare

https://www.chembuddy.com/pH-calculation-titration-curves-calculation

and

http://www.titrations.info/acid-base-titration-curve-calculation