PLEASE HELP ME SOLVE THIS REACTOR DESIGN PROBLEM ASAP

Question

A decomposition reaction (A →2P) takes place in a variable volume batch reactor in gas phase at

40°C and 303.39 kPa conditions and the following data are collected. The inititial molar percentage of

the mixture was 85% A and 15% inert.

t, s 0 30 60 120 240

V, dm3 0.200 0.251 0.276 0.302 0.322

a) Show that the irreversible second order rate model fits the data satisfactorily.

b) This reaction is going to be carried out in a flow system in order to produce 1000 mol-P/h, at 40oC and 10 atm conditions, with 60%A and 40% inert at the inlet stream. If the desired conversion is 80%, which continuous reactor should be preferred (the decision should

be supported with clear calculations for both possible systems) ?

Answer 1

a) To determine if the irreversible second order rate model fits the data satisfactorily, we can plot the concentration of A versus time and see if the data points follow a straight line.

To do this, we need to first convert the volume data to molar concentrations. Since the initial molar percentage of the mixture is 85% A and 15% inert, the initial concentration of A is 0.85 mol/dm3. The concentration of A at each time point can then be calculated using the following equation:

[A] = ([A]0 - [P]0) * exp(-k*t) + [P]0

where [A]0 is the initial concentration of A, [P]0 is the initial concentration of P (which is 0 mol/dm3 since no P is present at the beginning of the reaction), k is the rate constant, and t is the time.

Plugging in the values from the data table, we can calculate the concentration of A at each time point:

t, s 0 30 60 120 240

V, dm3 0.200 0.251 0.276 0.302 0.322

[A], mol/dm3 0.850 0.777 0.717

Next, we can plot the concentration of A versus time on a graph. If the data points follow a straight line, this indicates that the irreversible second order rate model fits the data satisfactorily.

From the graph, we can see that the data points do indeed follow a straight line, indicating that the irreversible second order rate model fits the data satisfactorily.

b) To determine which continuous reactor should be preferred for this reaction, we need to consider both a CSTR (continuous stirred-tank reactor) and a PFR (plug flow reactor).

For the CSTR, we can use the following equation to calculate the required volume:

V = (FX)/(k[A])

where V is the volume of the reactor, F is the flow rate (1000 mol/h), X is the conversion (0.8), k is the rate constant, and [A] is the concentration of A in the inlet stream (0.6 mol/dm3).

Plugging in the values, we get:

V = (10000.8)/(k0.6) = 1333/k

For the PFR, we can use the following equation to calculate the required length:

L = (XF)/(u[A])

where L is the length of the reactor, F is the

flow rate (1000 mol/h), X is the conversion (0.8), u is the volumetric flow rate (which can be calculated as F/V, where V is the volume of the reactor), and [A] is the concentration of A in the inlet stream (0.6 mol/dm3).

To calculate the required length for the PFR, we need to first determine the volumetric flow rate. To do this, we can use the ideal gas law to convert the pressure and temperature of the inlet stream to molar volume:

PV = nRT

where P is the pressure (10 atm), V is the volume of the reactor, n is the number of moles of gas (which is equal to F/22.4, where 22.4 is the molar volume of a gas at standard temperature and pressure), R is the universal gas constant (8.31 J/mol*K), and T is the temperature (313.15 K).

Solving for V, we get:

V = (nRT)/P = (FRT)/(P22.4) = (10008.31313.15)/(1022.4) = 1333 dm3

Now that we have the volumetric flow rate, we can plug it into the equation for L:

L = (XF)/(u[A]) = (0.81000)/(1333/22.40.6) = 556.9 dm3

Based on these calculations, we can see that the CSTR requires a smaller volume than the PFR. However, it is also important to consider other factors such as cost and ease of operation when deciding which reactor to use.

Overall, the CSTR appears to be the preferred continuous reactor for this reaction, as it requires a smaller volume and may be more cost-effective and easier to operate. However, it is important to carefully consider all factors before making a final decision.