Equilibrium conversion in reactor

Your Name]In summary, to find the equilibrium conversion of SO2 in a gas stream that enters a catalytic converter at 1 bar and 480 C, we can use the equilibrium constant expression and the ideal gas law to set up a system of equations. By comparing the initial number of moles of SO2 to the number of moles at equilibrium, we can calculate the equilibrium conversion. If pure oxygen is used, the maximum possible conversion of SO2 can be calculated by setting the mole fraction of oxygen to 1.
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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.
 

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  • #2


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
 

1. What is equilibrium conversion in a reactor?

Equilibrium conversion is the maximum percentage of reactants that can be converted into products in a chemical reaction under specific temperature and pressure conditions, where the rate of forward reaction is equal to the rate of reverse reaction.

2. How is equilibrium conversion determined?

Equilibrium conversion is usually determined experimentally by measuring the concentrations of reactants and products at different time intervals and calculating the percentage of conversion using the initial and final concentrations.

3. Why is equilibrium conversion important in reactor design?

Equilibrium conversion is important because it helps in determining the optimal conditions for a chemical reaction in a reactor, such as the temperature, pressure, and catalyst, to achieve the desired conversion rate and maximize the yield of the desired product.

4. Can the equilibrium conversion be altered or manipulated?

Yes, the equilibrium conversion can be altered by changing the temperature, pressure, or concentration of reactants and products in the reactor. Using a catalyst can also shift the equilibrium towards the desired product.

5. What is the relationship between equilibrium conversion and reaction rate?

There is an inverse relationship between equilibrium conversion and reaction rate. As the reaction rate increases, the equilibrium conversion decreases and vice versa. This is because at higher reaction rates, the reactants are consumed quickly, leading to a lower percentage of conversion at equilibrium.

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