Consider the following reactions:

$AB$

$B+MC$

Assume $M$ is present in great excess. The concentrations of $B$ and $C$ are zero at $t=0.$

$($a$)$ Write out the rate equations for $A,B$ and $C$

$($b$)$ Assuming the pseudo$-$steady $-$state approximation for $B,$ derive a set of equations for the time dependent variation in concentration of $A,B$ and $C$

$($c$)$ Make a sketch $($plot$)$ of the changes in concentrations of all three as a function of time.