Consider the reaction between NO2 and N2O4 in a closed container:
Initially, 1 mole of N2O4 is present. At equilibrium, α mole of N2O4 has dissociated to form NO2. (a) Derive an expression for KP in terms of a and P, the total pressure. (b) How does the expression in (a) help you predict the shift in equilibrium due to an increase in P? Does your prediction agree with Le Châtelier’s principle?
a)
Interpretation:
An expression for
Concept introduction:
Law of mass action: The rate of chemical reaction is directly proportional to the product of concentrations of reactant to products.
Multiple equilibria: If a reaction can be expressed as the sum of two or more reactions, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants of the individual reactions.
The equilibrium constant for two separate equilibrium constants are,
For overall reaction, the equilibrium constant
Therefore,
Calculating equilibrium concentration:
- Express the equilibrium concentrations of all species in terms of the initial concentrations and a single unknown x, which represents the change in concentration.
- Write the equilibrium constant expression in terms of the equilibrium concentrations. Knowing the value of the equilibrium constant, solve for x.
- Having solved for x, calculate the equilibrium concentrations of all species.
Explanation of Solution
For the given reaction,
Given: Initially
Construct ICE table as follows,
The total moles in the system =
Hence, expression for
b)
Interpretation:
The shift in equilibrium due to an increase in P has to be predicted and the prediction has to be agreed with Lee-Chatelier’s principle.
Concept introduction:
Law of mass action: The rate of chemical reaction is directly proportional to the product of concentrations of reactant to products.
Multiple equilibria: If a reaction can be expressed as the sum of two or more reactions, the equilibrium constant for the overall reaction is given by the product of the equilibrium constants of the individual reactions.
The equilibrium constant for two separate equilibrium constants are,
For overall reaction, the equilibrium constant
Therefore,
Calculating equilibrium concentration:
- Express the equilibrium concentrations of all species in terms of the initial concentrations and a single unknown x, which represents the change in concentration.
- Write the equilibrium constant expression in terms of the equilibrium concentrations. Knowing the value of the equilibrium constant, solve for x.
- Having solved for x, calculate the equilibrium concentrations of all species.
Explanation of Solution
For the given reaction,
Given: Initially
Rearranging
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