## timo86m 2 years ago for nin And using calc to derive this formula

1. timo86m

2. timo86m

@nincompoop

3. nincompoop

4. timo86m

Yes i remember integrating with time.

5. timo86m

The central science book is not that advanced then since it just gives you formulas but doesn't explain how to reach that conclusion

6. timo86m

calc 2 in this case. There is also some advanced wave function kinda stuff.

7. timo86m

in the electronic structure of matter chapter luckily it dont go too far. It just gives you equations you will use.

8. abb0t

Is this for thermodynamics? D:

9. abb0t

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: $[A] = [A]_0 e^{(-k_{1^{st}}t)}$

10. nincompoop

@abb0t I think what you did is the same to what I attached

11. abb0t

Oh. Lol. My bad. haha.