Solving the Isothermal Constant Volume A = B + C Reaction

In summary, an isothermal constant volume reaction is a chemical reaction that occurs at a constant temperature and volume, with no external work done on the system. The A = B + C reaction is solved using the law of mass action and rate law, while factors such as temperature, concentration, catalysts, and pressure can affect its rate. The equilibrium constant (K) for this reaction is calculated using the ratio or equilibrium expression of products and reactants. Real-world applications of solving this reaction include pharmaceutical production, food and beverage industry, and environmental science.
  • #1
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Homework Statement


Reaction: A = B + C

Reaction is run in an isothermal constant volume reaction vessel. Initially, before any reaction has occurred, the vessel is filled with pure A at 1 atm and 400K. The equilibrium conversion, epsilon and final pressure of the system is to be determined.


Homework Equations



I have no idea where to progress from where I am at. My attempt to the question is descried below.



The Attempt at a Solution




Component Initial Dissociation yi
A 1 1-epsilon (1-eps)/(1+eps)
B 0 epsilon eps/(1+eps)
C 0 epsilon eps/(1+eps)

Ka = Kp*Ky*Kf/Kf0

Kf0 based on fugacity at 1 atm
Kp = (P2/1)1
Ky = (eps^2/(1+eps)^2)
Kf = still unknown but based on (f/p)
Ka = 1.0

since ln(Ka1/Ka2) = integral(H/RT) dt = 0 for isothermal process

Ka1 = Ka2 where Ka = 1 for standard state of p=1 atm and T = 400K


Would anyone on here have any idea how to go about this question?
 
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  • #2



Thank you for your question. In order to determine the equilibrium conversion, epsilon, and the final pressure of the system, we need to use the equilibrium constant, Kc.

Kc = (^nb [C]^nc)/[A]^na

where and [C] are the molar concentrations of B and C, and [A] is the molar concentration of A. The subscripts nb and nc represent the stoichiometric coefficients of B and C in the reaction, while na is the stoichiometric coefficient of A.

Since the reaction is taking place in an isothermal and constant volume vessel, the molar concentrations are directly proportional to the partial pressures of each component. Therefore, we can rewrite the equilibrium constant as:

Kc = (Pb^nb Pc^nc)/Pa^na

where Pb, Pc, and Pa are the partial pressures of B, C, and A, respectively.

At equilibrium, the reaction will proceed until the equilibrium constant is reached. Therefore, we can set Kc equal to 1 and solve for epsilon:

1 = (epsilon^nb epsilon^nc)/(1-epsilon)^na

Solving for epsilon, we get:

epsilon = (1/2)^(1/na)

Since the initial pressure of A is 1 atm and the final pressure of the system is to be determined, we can use the ideal gas law to relate the initial and final pressures:

(Pa)V = (Pf)V

where V is the volume of the reaction vessel. Substituting in the initial and final pressures, we get:

(1 atm)(V) = (Pf)(V)

Solving for Pf, we get:

Pf = 1 atm

Therefore, the final pressure of the system will remain at 1 atm.

I hope this helps answer your question. Please let me know if you have any further inquiries.
 
  • #3


I would approach this problem by first understanding the basic principles and equations involved in isothermal constant volume reactions. From the given information, we know that the reaction is taking place at a constant temperature of 400K and in a constant volume vessel. This means that the pressure and volume will remain constant throughout the reaction.

Next, I would look at the equilibrium expression for this reaction, which is given by Ka = [C]/[A]. Since the initial concentration of B and C is 0, we can simplify this to Ka = [C]/[1]. We also know that the initial pressure of A is 1 atm, which means that the final pressure of the system will also be 1 atm.

To solve for the equilibrium conversion, we can use the equation epsilon = /+[C]. Since and [C] are both equal to epsilon, we can rewrite this as epsilon = epsilon/[epsilon+epsilon] = 1/2. This means that the equilibrium conversion is 50%.

Finally, to determine the final pressure of the system, we can use the ideal gas law, PV = nRT, where n is the number of moles of gas. Since the initial pressure and temperature are known, we can solve for the final number of moles using the ideal gas law. We can then use this number of moles to calculate the final pressure of the system, which we know is 1 atm. This will give us the final pressure of the system at equilibrium.

In summary, to solve for the equilibrium conversion and final pressure of the system in an isothermal constant volume reaction, we need to use the equilibrium expression, ideal gas law, and basic principles of isothermal reactions.
 

What is an isothermal constant volume reaction?

An isothermal constant volume reaction is a chemical reaction that occurs at a constant temperature and volume. This means that the total heat content of the reaction remains constant and no external work is done on the system.

How is the A = B + C reaction solved?

The A = B + C reaction is solved using the principles of the law of mass action and the rate law. These laws describe the relationship between the concentrations of reactants and products and the rate at which the reaction occurs. By manipulating these equations, the reaction can be solved for the concentrations of A, B, and C at any given time.

What factors affect the rate of the A = B + C reaction?

The rate of the A = B + C reaction can be influenced by factors such as temperature, concentration of reactants and products, presence of catalysts, and pressure. These factors can change the kinetics of the reaction and therefore affect the rate at which it occurs.

How is the equilibrium constant (K) calculated for the A = B + C reaction?

The equilibrium constant for the A = B + C reaction is calculated by taking the ratio of the concentrations of the products to the reactants at equilibrium. This can also be calculated using the equilibrium expression, which is the product of the concentrations of the products raised to their respective stoichiometric coefficients divided by the product of the concentrations of the reactants raised to their respective stoichiometric coefficients.

What are some real-world applications of solving the A = B + C reaction?

Solving the A = B + C reaction has many practical applications, including in the production of pharmaceuticals, food and beverage industry, and in environmental science. Understanding the kinetics and equilibrium of this reaction can help in the development of more efficient and sustainable processes in these industries.

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