A company wishes to develop a premium milk product. Their raw milk, which they want to convert

to a premium milk, contains $0\mathrm{.}001mo\frac{l}{L}$ of a soluble mineral $A.$ This mineral is undesired and is

unwanted in their premium milk product. They wish to reduce the concentration of $A$ in the raw milk

to $0\mathrm{.}0002mo\frac{l}{L},$ thus making the milk suitable for infants $($premium milk$).$

Engineers propose they convert $A$ to $R$ in a chemical reactor. This is because $R$ is not harmful to

infants. The reaction $A2R$ occurs in liquid phase in a CSTR reactor of $1000L.$ For the purpose of

analysing the reaction kinetics, the raw milk is fed to the reactor and the concentration of the

product $R$ at the outlet of the CSTR was measured. It was measured when the reaction was

refrigerated $(4C)$ and room temperature $(25C)$ as shown in table $1$ below.

Table $1$: Concentration of product $R$ under various conditions.

a$)$ What is the required conversion of A needed for their premium product?

b$)$ Determine the conversion of A for each condition in Table $1.$ Are they able to achieve

the required conversion at these temperatures?

c$)$ Show that the reaction is second order.

d$)$ Determine the activation energy and Arrhenius constant for the reaction.

e$)$ The maximum temperature that milk can be heated to is $70C.$ Determine the rate

constant for the reaction at $70C.$

f$)$ Calculate the conversion at the outlet of the reactor if the feed volumetric flow is $10$

$\frac{L}{m}in$ at $70C.$

g$)$ Determine the maximum volumetric flow rate that the reactor can be operated at and

achieve the desired conversion at $70C.$