research python chemistry 12 June 2017

# Chemical kinetics with python

## Exploring chemical reaction kinetics with Python

Chemical reactions is what nearly all branches of chemistry are dealing with on daily basis. They provide a fundamental framework to express observable changes of matter in a quantitative manner.

\begin{align} A & \xrightarrow{k_1} B \\ A & \xrightarrow{k_2} C \\ \end{align}

leading to the set of kinetic equations

\begin{align} \frac{d[A]}{dt} &= -(k_1 + k_2) [A] \\ \frac{d[B]}{dt} &= k_1 [A] \\ \frac{d[C]}{dt} &= k_2 [A] \\ \end{align}

with a solution new

\begin{align} [A] &= [A]_{0} e^{-(k_1 + k_2)t} \\ [B] &= \frac{k_1}{k_1 + k_2} [A]_{0} \left(1 - e^{-(k_1 + k_2)t}\right) \\ [C] &= \frac{k_2}{k_1 + k_2} [A]_{0} \left(1 - e^{-(k_1 + k_2)t}\right) \\ \end{align}

in python

import numpy as np
import scipy as sp

def function(args):
pass


or in fortran

use newmodule

write(*, *) "hello world"