P$2-6B_B$ The exothermic reaction

AlongrightarrowB$+C$

was carried out adiabatically and the following data recorded:

The entering molar flow rate of A was $300mo\frac{l}{m}in.$

$($a$)$ What are the PFR and CSTR volumes necessary to achieve $40\%$ conver$-$

sion? $(V_{PFR}=7\mathrm{.}2d{m}^3,V_{CSTR}=2\mathrm{.}4d{m}^3)$

$($b$)$ Over what range of conversions would the CSTR and PFR reactor vol$-$

umes be identical?

$($c$)$ What is the maximum conversion that can be achieved in a $10\mathrm{.}5-d{m}^3$

CSTR$?$

$($d$)$ What conversion can be achieved if a $7\mathrm{.}2-$dm$^3$ PFR is followed in series

by a $2\mathrm{.}4-d{m}^3$ CSTR$?$

$($e$)$ What conversion can be achieved if a $2\mathrm{.}4-d{m}^3$ CSTR is followed in a

series by a $7\mathrm{.}2-d{m}^3$ PFR$?$

$($f$)$ Plot ihe conversion and rate of reaction as a function of PFR reactor vol$-$

ume up to a volume of $10d{m}^3.$ P$11-6B_B$ In a certain chemical plant, a reversible fluid$-$phase isomerization

$AB$

is carried out over a solid catalyst in a tubular packed$-$bed reactor. If the reac$-$

tion is so rapid that mass transfer between the catalyst surface and the bulk

fluid is rate$-$limiting$,$ show that the kinetics are described in terms of the bulk

concentrations $C_A$ and $C_B$ by

$-r_A^{\text{'}\text{'}}=\frac{k_B[C_A-(\frac{1}{K})C_B]}{\frac{1}{K}+\frac{k_B}{k_A}}$

where $,-r_A^{\text{'}\text{'}}=$ moles of $A^{\text{'}}$ reacting per unit area catalyst per unit time

$k_A,k_B=$ mass transfer coefficients for A and $B$

$K=$ reaction equilibrium constant

It is desired to double the capacity of the existing plant by processing twice

the feed of reactant A while maintaining the same fractional conversion of $A$

to $B$ in the reactor. How much larger a reactor, in terms of catalyst weight, would

be required if all other operating variables are held constant? You may use the

Thoenes$-$Kramers correlation for mass transfer coefficients in a packed bed.

Describe the effects of the flow rate, temperature, particle size at conversion.