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49 Interpretation & The Use of Rate Law ITK-329 Kinetika & Katalisis Dicky Dermawan Chapter 3

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50 Conversion Moles of A consumed = Moles of A fed – Moles of A IN the reactor Batch Systems Flow Systems

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51 Typical Questions : 3.9 A first-order polymerization reaction is being run in a batch reactor. A concentration of mol/liter of monomer is loaded into the reactor, and then a catalyst is added to initiate the reaction. Experiments show that the reaction is 30% complete in 10 minutes. a. Calculate the rate constant b. Calculate the half-life c. How long will it take for the reaction to be 90% complete? d. How would the time in (c) change if you increased the concentration in the reactor to 0.16 mol/liter? e. Repeat for a second order reaction.

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52 Typical Questions (2) : 3.10 N 2 O 5 can be made via oxidation of ammonia over a platinum gauze. You do an experiment and find that you get 50% conversion of the ammonia with a 0.1 second residence time in the reactor at 1000 K. a. Calculate the rate constant for the reaction assuming that the reaction is first-order in the ammonia pressure and zero-order in oxygen pressure. b. How long of a residence time will you need to get 90% conversion at 1000 K? c. Now assume that the reaction is instead secondorder in the ammonia pressure. d. Estimate the rate constant for the reaction assuming 50% conversion in 0.1 second. Assume a stoichiometric feed at 1 atm pressure

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53 Kinetics from Minimal Number of Data L3.5 In a homogeneous isothermal liquid polymerization, 20% of the monomer disappears in 34 min for initial monomer concentration of 0.04 mol/L and also for 0.8 mol/L. What is the rate of disappearance of the monomer? L3.10 In units of moles, liters, and seconds, find the rate expression for the decomposition of ethane at 620 o C from the following information obtained at atmospheric pressure. The decomposition rate of pure ethane is 7.7%/sec, but with 85.26% inerts present the decomposition rate drops to 2.9%/sec.

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54 Kinetics from Minimal Number of Data L3.21 Find the first-order rate constant for the disappearance of A in the gas reaction 2 A > R if, on holding the pressure constant, the volume of the reaction mixture, starting with 80% A, decreases by 20% in 3 min. L3.22 Find the first-order rate constant for the disappearance of A in the gas reaction A > 1.6 R if the volume of the reaction mixture, starting with pure A, increases by 50% in 4 min. The total pressure within the system stays constant at 1.2 atm, and the temperature is 25 o C

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55 Kinetics from Minimal Number of Data: Reversible Reaction L3.9 The first-order reversible liquid reaction A R, C A0 = 0,5 mol/L, C R0 = 0 Takes place in a batch reactor. After 8 minutes, conversion of A is 33.3% while equilibrium conversion is 66.7%. Find the rate equation for this reaction

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56 Integration of a Rate Equation : Interpretation of Reaction Order L3.2 Liquid A decomposes by first order kinetics, and in a batch reactor 50% of A is converted in a 5-minute run. How much longer would it take to reach 75% conversion? L3.3 Repeat the previous problem for second-order kinetics

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57 Integration of a Rate Equation Assume that you are running a reaction A B that follows: Where r A is the rate of reaction in mol/(L.sec), T is temperature in Kelvin, R = cal./(mol.K) The temperatur varies during the course of the reaction according to: where t is time in second How long will it take to reduce the A concentration from 1 mol/L to 0,1 mol/L? For homogeneous reaction taking place in a batch reactor: For a constant volume batch reactor:

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58 Integration of a Rate Equation : Interpretation of Reaction Order L3.4 A 10-minute experimental run shows that 75% of liquid reactant is converted to product by a ½ order rate. What would be the amount converted in a half-hour run?

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59 Integration of a Rate Equation : Constant Volume vs Constant Pressure Batch Reactor L3.23 A zero-order homogeneous gas reaction A r R Proceeds in a constant-volume bomb, 20% inerts, and the pressure rises from 1 to 1.3 atm in 2 min. If the same reaction takes place in a constant-pressure batch reactor, what is the fractional volume change in 4 min if the feed is at 3 atm and consist of 40% inerts?

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60 Integration of a Rate Equation : Constant Volume vs Constant Pressure Batch Reactor L3.24 A zero-order homogeneous gas reaction A r R Proceeds in a constant-volume bomb, P = 1 at t = 0, and P = 1.5 when t = 1. If the same reaction, same feed composition, and initial pressure proceeds in a constant-pressure setup, find V at t = 1 if V = 1 at t = 0

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61 Integration of a Rate Equation : Constant Volume vs Constant Pressure Batch Reactor L3.25 The first-order homogeneous gaseous decomposition A 2.5 R Is carried out in an isothermal batch reactor at 2 atm with 20% inerts present, and the volume increases by 60% in 20 min. In a constant-volume reactor, find the time required for the pressure to reach 8 atm if the initial pressure is 5 atm, 2 atm of which consist of inerts.

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62 Integration of a Rate Equation : Constant Volume vs Constant Pressure Batch Reactor L3.26 The gas reaction 2 A R + 2 S Is approximately second order with respect to A. When pure A is introduced at 1 atm into a constant-volume batch reactor, the pressure rises 40% in 3 min. For a constant-pressure batch reactor, find: a. the time required for the same conversion b. The fractional increase in volume at that time.

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63 Multiple Reactions L3.16 Nitrogen pentoxide decomposes as follows: N 2 O 5 ½ O 2 + N 2 O 4 –r N 2 O 5 = (2.2x10 -3 min -1 ).C N 2 O 5 N 2 O 4 2 NO 2 K p = 45 mmHg Find the partial pressures of the contents of a constant- volume bomb after 6.5 hours if we start with pure at atmospheric pressure

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64 Multiple Reactions: L3.18 For the reactions in series: Find the maximum concentration of R and when it is reached if: a. k 1 = 2 k 2 b. k 1 = k 2

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