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**Interpretation & The Use of Rate Law**

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

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**Conversion Batch Systems Flow Systems**

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

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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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Typical Questions (2): 3.10 N2O5 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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**Kinetics from Minimal Number of Data**

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 620oC 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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**Kinetics from Minimal Number of Data**

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 25oC

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**Kinetics from Minimal Number of Data: Reversible Reaction**

The first-order reversible liquid reaction A R, CA0 = 0,5 mol/L, CR0 = 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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**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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**Integration of a Rate Equation**

For homogeneous reaction taking place in a batch reactor: For a constant volume batch reactor: Assume that you are running a reaction A B that follows: Where rA 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?

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**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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**Integration of a Rate Equation: Constant Volume vs Constant Pressure Batch Reactor**

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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**Integration of a Rate Equation: Constant Volume vs Constant Pressure Batch Reactor**

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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**Integration of a Rate Equation: Constant Volume vs Constant Pressure Batch Reactor**

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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**Integration of a Rate Equation: Constant Volume vs Constant Pressure Batch Reactor**

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: the time required for the same conversion The fractional increase in volume at that time.

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**Multiple Reactions L3.16 Nitrogen pentoxide decomposes as follows:**

N2O5 ½ O2 + N2O4 –rN2O5 = (2.2x10-3 min-1).CN2O5 N2O4 2 NO Kp = 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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**Multiple Reactions: L3.18 For the reactions in series:**

Find the maximum concentration of R and when it is reached if: k1 = 2 k2 k1 = k2

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