Assignment Problem: Modeling and Analysis of a First Order Chemical Reaction

You are tasked with designing a chemical reactor for the production of a desired compound through a firstorder chemical reaction. The reaction proceeds according to the following elementary reaction kinetics:

$AB$

Where, $A,$ is the reactant and $B,$ is the desired product.

Objective:

Your objective is to determine the concentration profile of$,$ A as a function of time within the reactor.

Problem Statement:

Consider a batch reactor with an initial concentration of $A(C{A}_0)$ of $2\mathrm{.}0mo\frac{l}{L}.$ The rate constant $(k)$ for the reaction is $0\mathrm{.}1s-1.$ You are required to model the concentration profile of A over a period of $10$ seconds using the fourth$-$order Runge$-$Kutta method.

Tasks:

a$)$ Formulate the first$-$order ordinary differential equation $($ODE$)$ governing the concentration of A with respect to time.

b$)$ Implement the fourth order Runge$-$Kutta method in Microsoft Excel to solve the ODE numerically.

c$)$ Create a time$-$step of $1$ second and calculate the concentration of $A$ at each time step up to $10$ seconds.

d$)$ Plot the concentration profile of $A$ as a function of time.

$1$

e$)$ Analyze, interpret and discuss any trends or observations observed in the concentration profile.