for nin And using calc to derive this formula

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for nin And using calc to derive this formula

Mathematics
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Other answers:

Yes i remember integrating with time.
The central science book is not that advanced then since it just gives you formulas but doesn't explain how to reach that conclusion
calc 2 in this case. There is also some advanced wave function kinda stuff.
in the electronic structure of matter chapter luckily it dont go too far. It just gives you equations you will use.
Is this for thermodynamics? D:
For a reaction of the form: A --> product a first order rate law takes the form: \[r = k_{1^{st}}[A]^1\] writing it in differentials, you get: \[\frac{ d[A] }{ dt } = -k_{1^{st}}[A]\] The minus sign as A is a reactant and so its concentration decreases with time (whici is the slope of a graph of [A] against time will be negativ when you graph it) The variables [A] and t can be separated to give: \[\frac{ 1 }{ [A] }d[A] = -k_{1^{st}}dt\] which CAN be integrated easily! \[\int\limits \frac{ 1 }{ [A] }d[A] = \int\limits -k_{1^{st}}dt\] this gives: \[\ln[A] = -k_{1^{st}}t + C\] The constant can be removed by supposing that at t = 0 since \[[A] = [A]_0\] which is the initial concentration of A giving us: \[\ln[A] = -k_{1^{st}}t + \ln[A]_0\] to simplify it a bit more to a form that might be more familiar to you is: \[[A] = [A]_0 e^{(-k_{1^{st}}t)} \]
@abb0t I think what you did is the same to what I attached
Oh. Lol. My bad. haha.

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