The following liquid$-$phase reactions are performed in a plug flow

reactor $($PFR$)$:

A $2$R r A$1=$ k $1$CA

A $3$S r A$2=$ k$2$ CA

For a residence time of $45$ s the conversion of reactant $$A$$ is

found to be $25\%$ and the ratio of moles of $$R$$ produced to moles

of $$S$$ produced is found to be $4$ to $1.$ TheQuestion $3$

The following liquid$-$phase reactions are performed in a plug flow

reactor $($PFR$)$:

$A2R,r_{A1}=k_1{C}_A$

$A3S,r_{A2}=k_2{C}_A$

For a residence time of $45s$ the conversion of reactant $\text{'}A\text{'}$ is

found to be $25\%$ and the ratio of moles of $\text{'}R\text{'}$ produced to moles

of $\text{'}S\text{'}$ produced is found to be $4$ to $1.$ The reactor feed is pure $\text{'}A\text{'}.$

$($a$)$ Show that the ratio of $k_1$ to $k_2$ is $6.$

$[10$ marks$]$

$($b$)$ Calculate $k_1$ and $k_2$

$[15$ marks$]$