For an exothermic reaction 𝐴 → 𝐵, 90kmol of B are to be produced while achieving90% conversion of A in an isothermal batch reactor operated at 500K. The reaction isstarted with pure A at the concentartion of 10kmol/m3. Determine the volume ofreactor and duration of batch operation.Additional information: CAo =1kmol/m3; 20% conversion is obtained in 20min while50% conversion is obtained in 80min. The reaction is suspected to be either firstorder or second order
Question
For an exothermic reaction 𝐴 → 𝐵, 90kmol of B are to be produced while achieving90% conversion of A in an isothermal batch reactor operated at 500K. The reaction isstarted with pure A at the concentartion of 10kmol/m3. Determine the volume ofreactor and duration of batch operation.Additional information: CAo =1kmol/m3; 20% conversion is obtained in 20min while50% conversion is obtained in 80min. The reaction is suspected to be either firstorder or second order
Solution
To solve this problem, we first need to determine the order of the reaction. We can do this by using the given conversion data.
For a first order reaction, the rate is proportional to the concentration of the reactant, i.e., -dCA/dt = kCA. Integrating this equation from CA0 to CA gives us the time required for a certain conversion, which is t = (1/k) * ln(CA0/CA).
For a second order reaction, the rate is proportional to the square of the concentration of the reactant, i.e., -dCA/dt = kCA^2. Integrating this equation from CA0 to CA gives us the time required for a certain conversion, which is t = (1/kCA0) * (CA0 - CA).
Given that 20% conversion is obtained in 20 min and 50% conversion is obtained in 80 min, we can set up two equations and solve for k.
For the first order reaction: 20 = (1/k) * ln(1/0.8) 80 = (1/k) * ln(1/0.5)
For the second order reaction: 20 = (1/k) * (1 - 0.8) 80 = (1/k) * (1 - 0.5)
Solving these equations will give us the value of k for both the first and second order reactions. The value of k that best fits the given data will determine the order of the reaction.
Once we know the order of the reaction, we can calculate the volume of the reactor and the duration of the batch operation.
The volume of the reactor can be calculated using the equation V = n/CA, where n is the number of moles of B to be produced and CA is the concentration of A.
The duration of the batch operation can be calculated using the time equations derived above for the first and second order reactions.
Please note that the initial concentration of A (CA0) is given as 10 kmol/m3, not 1 kmol/m3 as stated in the additional information.
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