Timeline for Calculation of Degree of Dissociation from Ostwald's Dilution Law
Current License: CC BY-SA 4.0
20 events
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| May 6, 2020 at 16:00 | comment | added | MaxW | @BuckThorn - I did number the last two equations, otherwise the equations have kept their numbering. In one of the revisions I did move the equations around, but I kept the numbering. // I added a second answer which is much more the the OP's question. My final point there was if you're going to use the approximation, then check the error bound, why not just use the quadratic to begin with since it gives the exact answer for a pittance of extra work. | |
| May 6, 2020 at 13:04 | comment | added | Buck Thorn♦ | I think you changed the equation labels. My question remains: the final series expansion does not seem an advantage over the exact solution (it seems even more complicated to compute). And the advantage of the simplified formula is that you can quickly evaluate it in your calculator or even your head (back when people knew how to estimate square roots in their heads). The advantage is more or less null in our day of broadly available computing power. | |
| May 5, 2020 at 20:46 | comment | added | MaxW | @BuckThorn - The point of the last section was to go from equation (8) which is the quadratic solution to equation (13) - never intended to stop at equation (9). Even with just two terms in the denominator equation (13) works very well for $K_d/c_0 < 0.5$. Using all three terms in equation (13) gives you near perfect values up to $K_d/c_0 = 1$. | |
| May 5, 2020 at 20:41 | history | edited | MaxW | CC BY-SA 4.0 |
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| May 5, 2020 at 19:16 | comment | added | Buck Thorn♦ | +1 I found this a useful answer, I never thought about the usefulness of the estimate to bracket the true value. But I do wonder what is the usefulness of the final exercise. Eq 11 is certainly not an improvement over Eq 9 in terms of simplicity. | |
| May 5, 2020 at 8:23 | history | edited | MaxW | CC BY-SA 4.0 |
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| May 5, 2020 at 8:16 | comment | added | MaxW | Ok, I've done a major revision to the answer, Hopefully the revised version is easier to understand. | |
| May 5, 2020 at 8:12 | history | undeleted | MaxW | ||
| May 5, 2020 at 8:12 | history | edited | MaxW | CC BY-SA 4.0 |
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| May 5, 2020 at 7:25 | history | deleted | MaxW | via Vote | |
| May 5, 2020 at 7:25 | history | edited | MaxW | CC BY-SA 4.0 |
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| May 5, 2020 at 4:46 | comment | added | MaxW | @LimboProductions - I'm trying to work out a series expansion now for the exact expression. Also the exact value is easily obtained by solving a quadratic equation. | |
| May 5, 2020 at 4:30 | comment | added | Amadeus | @MaxW, Then if the approximation shows that dissociation is, say, 13%, but as the real value will be lesser, let's say it is 8-9%. Here, in reality we can use the approximation but we would think otherwise. (I am assuming we have no way to calculate how much lower would the actual value be, or even an ballpark estimate, so correct me if I am wrong in assuming this) | |
| May 5, 2020 at 3:26 | comment | added | MaxW | @LimboProductions - I agree that I need to make the argument clearer. The gist is that the approximation assumes that little dissociation has occurred so the fraction dissociated is much less than 1. So if the approximation says that 1% has dissociated, the exact solution will show that slightly less has. So it is reasonable to use the approximate value to test the hypothesis. | |
| May 5, 2020 at 3:15 | comment | added | ACR | @LimboProductions, read both answers carefully especially the last paragraph of my answer. You have a misconception regarding this circular argument. | |
| May 5, 2020 at 2:49 | comment | added | Amadeus | I still don't understand how the central question of why we think it's okay to use alpha- prime which we derive through an approximation instead of alpha to judge whether the approximation was correct in the first place | |
| May 5, 2020 at 1:54 | history | edited | MaxW | CC BY-SA 4.0 |
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| May 5, 2020 at 1:17 | comment | added | MaxW | @M.Farooq - It is the difference between equations 5 and 6 that is important. Note alpha and alpha-prime are calculated and that alpha-prime > alpha always. | |
| May 5, 2020 at 1:13 | comment | added | ACR | I am confused, what is the conceptual difference between equation (2) (3) and (8)? It seems like a circular argument. | |
| May 4, 2020 at 20:34 | history | answered | MaxW | CC BY-SA 4.0 |