Equilibrium conversion in reactor

[member 392791]

Homework Statement

The gas stream from a sulfur burner is composed of 15-mol% SO2, 20-mol% O2, and 65-mol% N2. This gas stream at 1 bar and 480 C enters a catalytic converter, where the SO2 is further oxidized to SO3. Find the equilibrium conversion of SO2. The equilibrium constant for the reaction

SO2 + 1/2 O2 ⇔SO3

is 87.824 at 480C. What would be the equilibrium conversion of the reactor if pure oxygen were used under the same conditions?

Homework Equations

The Attempt at a Solution

I am not sure if I am going about this the right way, but I am wondering if I am how I can obtain a numerical solution for this non-linear algebraic equation, not sure how to use MATLAB or polymath to solve it.

 

[KataKoniK]

Thank you for your question. To solve this problem, we can use the equilibrium constant expression:

Kc = [SO3]/[SO2][O2]^(1/2)

At equilibrium, the concentrations of the reactants and products will be related by this equilibrium constant. We can set up a system of equations to solve for the equilibrium conversion of SO2:

1. At 1 bar and 480 C, the total pressure is equal to the partial pressures of each component:

Ptotal = Pso2 + Po2 + Pn2

2. The partial pressure of each component can be calculated using the ideal gas law:

P = nRT/V

where n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and V is the volume.

3. The equilibrium constant expression can be rewritten in terms of partial pressures:

Kc = (Pso3)/(Pso2 * Po2^(1/2))

4. Using the mole fractions given in the problem, we can calculate the number of moles of each component in the gas stream:

nso2 = (15/100)*n
no2 = (20/100)*n
nn2 = (65/100)*n

5. Substituting these values into the ideal gas law and the equilibrium constant expression, we can set up the following system of equations:

Ptotal = (15/100)*nRT/V + (20/100)*nRT/V + (65/100)*nRT/V
Kc = (Pso3)/(Pso2 * Po2^(1/2))

6. We can solve for the number of moles of SO3 using the equilibrium constant expression:

nso3 = (Kc * Pso2 * Po2^(1/2))/Ptotal

7. Finally, we can calculate the equilibrium conversion of SO2 by comparing the initial number of moles to the number of moles at equilibrium:

Conversion = (nso2 - nso3)/nso2

To calculate the equilibrium conversion if pure oxygen is used, we can follow the same steps but set the mole fraction of oxygen to 1 and the mole fraction of SO2 to 0. This will give us the maximum possible conversion of SO2.

I hope this helps you solve the problem. If you need further assistance, please don't hesitate to ask.

Best regards