The irreversible isomerization, $AB,$ was carried out in a batch reactor and the following concentration$-$

time data were obtained:

Reaction rate in batch reactor defines with the following equation;

$-r_A=\frac{d{C}_A}{dt}=-k{C}_A^n$

a$)$ Construct a cubic interpolation polynomial that defines the concentration as a function of time,

$C_A(t).$

b$)$ Differentiate the polynomial constructed in part $($a$),$ and then use this equation to find the $d\frac{C_A}{d}t$ at $t$

values given in the above table.

c$)$ Using the $d\frac{C_A}{d}t$ from $($b$)$ and $C_A$ from the given table, determine the reaction order $n$ and the

specific reaction rate $k$ in appropriate units using linear regression. Do all your calculations by

hand. In your hand calculations $($for Problem $2)$ use $4$ digits arithmetics.