Reaction Engineering I, Problem Set 1

Mass Balances in Batch and Steady State Isothermal Reactors

1. Show that for a first order reversible reaction A  B, the rate of reaction
   dt
   dCA
   can be
   expressed as the product of a constant, multiplied by the driving force
   ( ) CA CA,eq
   , where
   CA,eq is the equilibrium concentration of component A. Assume that the initial
   concentration of B is zero and that the temperature is constant.
2. A CSTR is used to decompose a dilute solution of A by a first order irreversible reaction.
   The value of the kinetic constant is 3.45 hr-1
   . The reactor volume is 10 m3
   . Calculate the
   flow rate of feed solution that can be treated if 95% decomposition is required? Neglect
   any volume change upon reaction.
3. What volume of reactor would be required to achieve the same conversion in a plug flow
   reactor, using the same volumetric flow rate?
4. Repeat problem 2 and 3 for xA = 0.5. Explain qualitatively the change in the difference
   between the sizes of the CSTR and PFR.
5. The liquid phase reactions:
   i. 2A  products, rA = k CA
   2
   ii. A + B  products, rA = k CA CB
   iii. 3A  products rA = k CA
   3
   are separately carried out in isothermal plug-flow reactors at steady state. Assuming
   constant mass density, derive expressions showing how the flow rate nA,e (at which ‘A’
   leaves the reactor) is related to reactor volume. P across the reactor may be neglected.
6. For the same liquid phase reactions as in problem 5, derive expressions showing how in a
   batch system the final conversion is related to reaction time. Compare these expressions
   with those found in problem 5.

Sample Solution