[amk0713]

Hi there. I'm just hoping to get a bit of clarification on this, as I learn best when I understand why a math equation is, rather than simply what happens.

What is the mathematical purpose behind ln when applied to chemical equations? For example, the equation for standard free energy as it relates to K:  :delta: G^o=-RTlnK. I understand that the result of lnx can be taken as the rate of growth to reach x, but how does this apply to that equation?

Thank you.

[Arkcon]

So, the question is, why does the function, described by the equation, increase logarithmically?  As opposed to, I would guess, linearly, or parabolically, or by some higher order polynomial?  Well, that's just kinda how it works, doesn't it?  Consider, instead of a purely chemical process, instead a biological process -- simple cells, yeast or bacteria, grow logarithmically, at least until they deplete their environment.  Why?  Because the same growth, applies to each daughter cell, and the parent cell, so the simple addition just expodes -- well, logarithmically.    I'm guessing, logrithmic propagation in the natural world, made it interesting, and mathematical theory was created around it, and then applied to phenomena that can be modeled by such a function.

[aldoxime_amine]

Practical examples of exponential growth or decay are R-C,R-L charge,discharge, all first order reactions, velocity of a falling rain drop etc

Exponential behavior is very easy to understand "practically". For example, in case of the falling rain drop, the faster it falls, the more does the wind oppose its motion, so that when a stage is reached when the opposition equals its weight, there is no acceleration, no more increase in opposition, resulting in achievement of terminal velocity.