Nov 25 2016

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CRE – 25.11.16 - Solutions 1 096116 Chemical Reaction Engineering 25 November 2016 Family name _________________________________________________ First name _________________________________________________ ID number _________________________________________________ Signature _________________________________________________ Please, consider that the sum of perc entages of proposed exercises (5 ) is equal to 110%. This means that the maximum mark you can reach is 16.5. Remember to write on the top of each sheet you submit: your name, ID number, and signature. Use of mobile phones, tablets and/or internet connection is not allowed. 1. Reaction rate law from experimental data (20%) The following aqueous reaction 𝐴𝐴↔ 𝑅𝑅+ 𝑆𝑆 proceeds according to the data reported in the table on the right. Assuming that at time 𝑡𝑡= 0 the initial concentration of species are 𝐶𝐶𝐴𝐴 0 = 0.1863 𝑚𝑚𝑚𝑚𝑚𝑚/𝑚𝑚, 𝐶𝐶𝑆𝑆 0 = 55 𝑚𝑚𝑚𝑚𝑚𝑚/𝑚𝑚 and 𝐶𝐶𝑅𝑅 0 = 0, find the rate equation and t he corresponding kinetic constant. Please describe and justify every simplifying assumption accounted for. Solution From the data provided in the table, it is evident that the reaction reached thermodynamic equilibrium. Thus, a s a first assumption it is obvious to consider the reaction law corresponding to a molecular reaction, i.e.: 𝑟𝑟= 𝑘𝑘�𝐶𝐶𝐴𝐴− 𝐶𝐶𝑅𝑅𝐶𝐶𝑆𝑆 𝐾𝐾𝑒𝑒𝑒𝑒 � From the data at 𝑡𝑡= ∞ we can estimate the equilibrium conversion and then easily calculate the equilibrium constant in the reaction rate above. In particular, at equilibrium we have that 𝑟𝑟= 0, thus: 𝑘𝑘�𝐶𝐶𝐴𝐴,𝑒𝑒𝑒𝑒 2 − 𝐶𝐶𝑅𝑅,𝑒𝑒𝑒𝑒𝐶𝐶𝑆𝑆,𝑒𝑒𝑒𝑒 𝐾𝐾𝑒𝑒𝑒𝑒 � = 𝑘𝑘�𝐶𝐶𝐴𝐴 0�1 − 𝑋𝑋𝑒𝑒𝑒𝑒�− 𝐶𝐶𝐴𝐴 0�𝑀𝑀− 𝑋𝑋𝑒𝑒𝑒𝑒�𝐶𝐶𝐴𝐴 0𝑋𝑋𝑒𝑒𝑒𝑒 𝐾𝐾𝑒𝑒𝑒𝑒 � = 0 Where for convenience we defined 𝑀𝑀= 𝐶𝐶𝑆𝑆 0/𝐶𝐶𝐴𝐴 0. From the equation above, we have: 𝐾𝐾𝑒𝑒𝑒𝑒= 𝐶𝐶𝐴𝐴 0𝑋𝑋𝑒𝑒𝑒𝑒�𝑀𝑀− 𝑋𝑋𝑒𝑒𝑒𝑒� 1 − 𝑋𝑋𝑒𝑒𝑒𝑒 Time [min] CA [mol/l] 0…