Reactant A decomposes according to the following first-order, irreversible, liqu

Question

Reactant A decomposes according to the following first-order, irreversible, liquid-phase reaction. A (1) rightarrow B (1) +C (g) Components A and B are nonvolatile liquids. The product C is a gas. The following data are available. Rare constantt at 120degreeC, k = 0.80 hr^-1 volumeetric flow rate of entering feed, vo = 172 L/hr The feed stream is pure A. If the reaction is performed in a single CSTR at 120degreeC, the reactor volumee (m3) required for 95percentage conversion is about A. 4.10B 3.40C 2.75D 0.21

Explanation / Answer

For a CSTR, the chaacteristic Equation is given by

T= CAOXA/-rA   (1)

The rate constant suggests the reaction to be first order.

Where CAO= initial concentration XA= conversion , CA= concentration at any space time, T= CAO*(1-XA), -rA= KCA= KCAO*(1-XA), K =rate constant =0.8/hr

CA= CAO*(1-XA)

T= V/Vo , V= volume of Reactor and Vo= volumetric flow rate =175L/hr

XA= conversion =0.95

Eq.1 becomes   T= CAOXA/(K*(1-XA),   KT= XA/(1-XA)=

0.8*T= 0.95/(1-0.95) =19

T= 19/0.8 =23.75

V/Vo= 23.75 and V= 23.75*175 L=4156.25 L= 4.156 m3

A is the correct answer

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