Timeline for Simplification of the ratio between series
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 15 at 9:00 | comment | added | redib | @EricSnyder, I actually made a program to calculate the titration curves, and it can be found here: Chemistry Calculators. (Be aware that it is "pay what you want".) | |
| Mar 15 at 8:57 | comment | added | redib | @EricSnyder, Based on a couple of equations from the book ”Principles of Quantitative Chemical Analysis” by Robert de Levie, 1997, you can derive the following equations, that describe a polyprotonic acid titrated with NaOH: $$V_b=V_a\frac{\sum_{i=0}^nK_t(i)[H^+]^{n-i}(-[H^+]^2+iC_a[H^+]+K_w)}{\sum_{i=0}^{n}K_t(i)[H^+]^{n-i}([H^+]^2+C_b[H^+]-K_w)}$$ $$\sum_{i=0}^{n}K_t(i)[H^+]^{n-i}\left(V_t[H^+]^2+\left(V_bC_b - iV_aC_a\right)[H^+]-K_wV_t\right)=0$$ The derivation I have made for these formulas is currently written in Danish, but I will happily translate it into English, and send it to you | |
| Mar 15 at 8:55 | comment | added | redib | @EricSnyder, I thought it couldn't be simplified any further, but i keep waking in the middle of the night, thinking i might finally have figured it out, but sadly my ideas never amount to any good solution. I thought it would be a sigmoid too! And it turns out that around the equivalence point, it can be approximated by an inverse sigmoid, as given by the Henderson-Hasselbach equation. But this idea sadly falls apart when moving away from the equivalence point, and especially when working with polyhydronic/polyprotonic acids or bases. | |
| Mar 15 at 0:03 | comment | added | Eric Snyder | Welcome to MSE! As a chemist, I'd love to see how you got to this from a titration curve, in particular wondering where the quadratic functions are coming from (are you accounting for fugacity etc? That might be the source). I can also say that I cannot imagine this expression has a "happy" solution; partial summations usually don't, and the necessity of specific values of $k_i$ mean you can't use a CAS easily either. The "ideal" titration curve ought to be a sigmoid of some sort, though; given it's usually pH on the $y$ axis, I'd expect one of the exponential-based sigmoids. | |
| S Mar 14 at 19:36 | review | First questions | |||
| Mar 14 at 19:41 | |||||
| S Mar 14 at 19:36 | history | asked | redib | CC BY-SA 4.0 |