Chapter 15: Problem 76
When heated, ammonium carbamate decomposes as follows: $$ \mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s) \rightleftarrows 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) $$ At a certain temperature, the equilibrium pressure of the system is 0.318 atm. Calculate \(K_{p}\) for the reaction.
Short Answer
Expert verified
\(K_p = 0.00476\)
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ammonium Carbamate Decomposition
Ammonium carbamate is a compound made of ammonium ions and carbamate ions. When heated, it readily decomposes into ammonia (\(\mathrm{NH}_{3}\)) and carbon dioxide (\(\mathrm{CO}_{2}\)).
The decomposition reaction is represented as follows: \[ \mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s) \rightleftarrows 2 \mathrm{NH}_{3}(g) + \mathrm{CO}_{2}(g) \] This reaction involves a solid reacting to form gaseous products. A fascinating aspect of this reaction is how it shifts from a single-phase (solid) to a gas-phase equilibrium when heated.
This means that the decomposition can be monitored by looking at the pressures of the gases produced.
The decomposition reaction is represented as follows: \[ \mathrm{NH}_{4} \mathrm{CO}_{2} \mathrm{NH}_{2}(s) \rightleftarrows 2 \mathrm{NH}_{3}(g) + \mathrm{CO}_{2}(g) \] This reaction involves a solid reacting to form gaseous products. A fascinating aspect of this reaction is how it shifts from a single-phase (solid) to a gas-phase equilibrium when heated.
This means that the decomposition can be monitored by looking at the pressures of the gases produced.
Equilibrium Constant
The equilibrium constant (\(K_p\)) is a value that expresses the ratio of the concentrations of products to reactants for a reaction at equilibrium.
In the context of gas-phase reactions, like the decomposition of ammonium carbamate, \(K_p\) is determined using the partial pressures of the gaseous components.
\(K_p\) provides important information about the position of equilibrium and the extent of the reaction. To express \(K_p\) for the decomposition reaction, we only consider the gases. Solids are not included in the expression for equilibrium constants.
Thus, the \(K_p\) expression for our reaction is: \[ K_p = \frac{(P_{\mathrm{NH}_3})^2 \times P_{\mathrm{CO}_2}}{1} \] This formula essentially describes how the partial pressures are related in equilibrium.
In the context of gas-phase reactions, like the decomposition of ammonium carbamate, \(K_p\) is determined using the partial pressures of the gaseous components.
\(K_p\) provides important information about the position of equilibrium and the extent of the reaction. To express \(K_p\) for the decomposition reaction, we only consider the gases. Solids are not included in the expression for equilibrium constants.
Thus, the \(K_p\) expression for our reaction is: \[ K_p = \frac{(P_{\mathrm{NH}_3})^2 \times P_{\mathrm{CO}_2}}{1} \] This formula essentially describes how the partial pressures are related in equilibrium.
Partial Pressures
Partial pressure is the pressure that a single gas in a mixture would exert if it occupied the entire volume by itself.
For gas reactions, understanding partial pressures helps in calculating equilibrium constants like \(K_p\).
Each gas in the mixture contributes to the total pressure depending on its mole fraction and individual properties. In the reaction of ammonium carbamate, as decomposition occurs, the total pressure measured arises from the partial pressures of ammonia and carbon dioxide.
By considering the reaction stoichiometry, we can determine the contribution of each gas to the total pressure and solve for their partial pressures.
This is crucial for accurately determining the equilibrium constant.
For gas reactions, understanding partial pressures helps in calculating equilibrium constants like \(K_p\).
Each gas in the mixture contributes to the total pressure depending on its mole fraction and individual properties. In the reaction of ammonium carbamate, as decomposition occurs, the total pressure measured arises from the partial pressures of ammonia and carbon dioxide.
By considering the reaction stoichiometry, we can determine the contribution of each gas to the total pressure and solve for their partial pressures.
This is crucial for accurately determining the equilibrium constant.
Chemical Equilibrium
Chemical equilibrium describes a state in which the rate of the forward reaction equals the rate of the reverse reaction.
At equilibrium, the concentrations of reactants and products remain constant over time. For ammonium carbamate decomposition, even as its solid form continues to break down to form gases, some of the gaseous molecules recombine to reform the solid.
Equilibrium is reached when these happenings balance out.
At this point, the measurable pressures of ammonia and carbon dioxide become constant.
This constancy allows us to calculate important values such as \(K_p\). The concept of chemical equilibrium is pivotal in understanding how reactions proceed and the factors influencing their dynamics.
At equilibrium, the concentrations of reactants and products remain constant over time. For ammonium carbamate decomposition, even as its solid form continues to break down to form gases, some of the gaseous molecules recombine to reform the solid.
Equilibrium is reached when these happenings balance out.
At this point, the measurable pressures of ammonia and carbon dioxide become constant.
This constancy allows us to calculate important values such as \(K_p\). The concept of chemical equilibrium is pivotal in understanding how reactions proceed and the factors influencing their dynamics.
