HOMEWORK USING MATLAB

The expression for the rate of monomer consumption is given by:

$Rp=k_p(\frac{f{k}_d}{k_i}{)}^{\frac{1}{2}}[I{]}^{\frac{1}{2}}[M]$

It is often more convenient to work in terms of monomer conversion X$.$ By making use of the definition of conversion:

$x=\frac{M_0-M}{M_0}$

Equation $2$ can be used to rewrite equation $1$ to be as follow

$\frac{dx}{dt}=k_p(\frac{f{k}_d}{k_l}{)}^{\frac{1}{2}}[I{]}^{\frac{1}{2}}(1-x)$

We can solve the integral explicitly to get:

$x=1-$exp$\{(\frac{2k_p}{k_d})(\frac{f{k}_d}{k_t})[I{]}_0^{\frac{1}{2}}[exp(\frac{-k_{dt}}{2})-1]\}$

a$)$ Write MATLAB code to plot conversion versus time by using equation number $4.$ Use the below parameters and vary $"k_d"$ values as indicated in the table to generate three plots in one figure. You need to submit the MATLAB code and the results $($one figure with three plots$).$

b$)$ Comment on your results.

$\backslash$table$[[$Parameter$,$Values$],[k_p,1900\frac{L}{M}$oles