Question

Derive equation of exist concentration from reactor starting from zero order equation

Answer 1

The reactor is assumed to CSTR

For a CSTR operated under steady state conditions

Rate of moles of A reactant in (FA)= Rate of moles of reactants out (FA)+ rate of loss of reactant due to Zero order reaction

FAO= FA+(-rA)V (1)

For a first order reaction (-rA)= K

FA =Molar flow rate of A at any time T =FAO*(1-XA)

FAO= initial molar flow rate of A

FAO= FAO*(1-XA)+ KV

FAOXA= KV (1)

but T= space time, =V/VO, VO= Volumetric flow rate of reactant =VCAO/FAO

FAO= VCAO/T ,CAO= Initial concentration of reactant A

V= Volume of reactor and XA = Conversion

Eq.1 becomes

(VCAO/T )*XA= KV

T= CAOXA/K

for a PFR

The concentration changes along the length of the reactor and hence balance will have to be written for a differential volume of element

FA= FA+dFA+ KdV

dFA= KdV

FA= FAO*(1-XA)

dFA= FAO*(-dXA)

-dFA= FAO*dXA

FAO*dXA= KdV

dV= FAO*dXA/K

Intergrating V= (FAO/K)*dXA