$($a$)$ Define extent of reaction. Stanting with the expression for the extent of reactican derve the expression for the maximum extent of reaction. $(2$ Marlas$)$

b$)$ The oxidation of $A$ to $B$ proceeds according to the equation

$2A+O_{2}2B$

The feed to the reactor contains $100$gmol of A and $100$gmol of $O_2.$ The reaction proceeds to a point where the fractional conversion of the limiting reactant is $50\%.$

a$)$ Find the maximum extent of reaction for $A.$

b$)$ Find the maximum extent of reaction for $O_2.$

c$)$ Find the product composition in terms of the mole fractions for all the product components. Marks$)$