QUESTION $4$

Answer ALL parts.

A reaction $($irreversible$,$ in liquid phase$)$ represented below takes place with takes place with equal initial concentrations of the two reagents:

$A+B2P$

It is known that a second order rate law is a good model.

$-r_A=k{C}_A{C}_B$

The patent description of this reaction says that with initial concentrations of A and $B$ of $2\mathrm{.}75mo\frac{l}{L}($dissolved in an organic solvent$)$ in a test tube at $70C$ after $1\mathrm{.}5$ hours reaction time there were $3\mathrm{.}11mo\frac{l}{L}$ of the product. The activation energy is $100k\frac{J}{m}ol.$

a$.$ Write the material balance to a batch reactor $($the lab test tube$)$ and from the information given in the patent determine the rate constant at $70C.$

$[50$ Marks$]$

b$.$ If the reaction is to be carried out at $95C$ how would the rate constant change?

$[20$ Marks$]$

c$.$ If the cleaning time per batch is $10$ minutes and a pump with a volumetric flowrate of $0\mathrm{.}5\frac{L}{m}in$ is used to load and unload the test tube, what is the working volume required to achieve a desired productivity of $0\mathrm{.}002mo\frac{l}{s}$ over a cycle time.

$[30$ Marks$]$

Arrhenius equation: $k=k_0{e}^{\frac{-E_A}{R(T_0-T)}}$

Ideal gas constant: mol. $K$