Dec 12 2014

Pagina 1

CRE – 12.12.14 - Exam A 096116 Chemical Reaction Engineering 12 December 2014 Exam A Family name _________________________________________________ First name _________________________________________________ ID number _________________________________________________ Signature _________________________________________________ This is just an example of possible exercises. Each exercise has a different weight (reported in terms of a percentage). Obviously, in the real written examination the sum of percentages of proposed exercises will be equal to 100%. The exercises reported in this example refer only to the first part of the course (homogeneous, ideal reactors). 1. Analysis of experimental data (15%) The first-order reversible liquid reaction 𝐴𝐴↔ 𝑅𝑅 takes place in a batch reactor. The initial concentration of A is equal to 0.5 mol/l. No R is present at initial time. After 8 minutes, the measured conversion of A is 33.3%, while the equilibrium conversion is 66.7%. Find the reaction rate expression for this reaction. Solution For a first order reversible reaction, the reaction rate is given by: 𝑟𝑟= 𝑘𝑘𝑓𝑓𝐶𝐶𝐴𝐴− 𝑘𝑘𝑏𝑏𝐶𝐶𝑅𝑅 Thus, our objective is to determine the values of kinetic constants 𝑘𝑘𝑓𝑓 and 𝑘𝑘𝑏𝑏. The integrated conversion equation in a batch reactor (constant volume because it is a liquid) Is given by: −𝑙𝑙𝑙𝑙�1 − 𝑋𝑋 𝑋𝑋𝑒𝑒𝑒𝑒 � = �𝑘𝑘𝑓𝑓+ 𝑘𝑘𝑏𝑏�𝑡𝑡 Replacing values, we then find: 1 CRE – 12.12.14 - Exam A −𝑙𝑙𝑙𝑙�1 − 33.3 66.7� = 8�𝑘𝑘𝑓𝑓+ 𝑘𝑘𝑏𝑏� 𝑘𝑘𝑓𝑓+ 𝑘𝑘𝑏𝑏= 𝑙𝑙𝑙𝑙2 8 = 0.086625 1 𝑚𝑚𝑚𝑚𝑙𝑙 Now, from the thermodynamics we know that: 𝐾𝐾𝑒𝑒𝑒𝑒= 𝑘𝑘𝑓𝑓 𝑘𝑘𝑏𝑏 = 𝐶𝐶𝑅𝑅 𝑒𝑒𝑒𝑒 𝐶𝐶𝐴𝐴 𝑒𝑒𝑒𝑒= 𝐶𝐶𝐴𝐴 0𝑋𝑋𝑒𝑒𝑒𝑒 𝐶𝐶𝐴𝐴 0�1 − 𝑋𝑋𝑒𝑒𝑒𝑒� = 𝑋𝑋𝑒𝑒𝑒𝑒 1 − 𝑋𝑋𝑒𝑒𝑒𝑒 = 66.7 33.3 = 2 Thus: 𝑘𝑘𝑓𝑓 𝑘𝑘𝑏𝑏 = 2 Solving the two equations reported above: ⎩ ⎨ ⎧ 𝑘𝑘𝑓𝑓 𝑘𝑘𝑏𝑏 = 2 𝑘𝑘𝑓𝑓+ 𝑘𝑘𝑏𝑏= 𝑙𝑙𝑙𝑙2 8 gives: �𝑘𝑘 𝑓𝑓= 0.028875 𝑚𝑚𝑚𝑚𝑙𝑙−1 𝑘𝑘𝑏𝑏=…