Chapter 15: Problem 30
The following equilibrium constants were determined at
Short Answer
Expert verified
The equilibrium constant is .
Step by step solution
01
Understand the given reactions
We are provided with two reactions and their equilibrium constants: with and with . We are tasked with finding the equilibrium constant for the overall reaction.
02
Identify the overall reaction
The target reaction is . This reaction can be obtained by summing the two given reactions.
03
Add the reactions
Add the two reactions given: and . Doubling the second reaction and adding to the first gives .
04
Calculate the overall equilibrium constant
When reactions are added, their equilibrium constants multiply. Therefore, the overall equilibrium constant is . Substitute the known values: .
05
Compute the final result
Calculate . Thus, . Final calculation gives .
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chemical Equilibrium
Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products. When a reaction reaches this state, we say the reaction has achieved equilibrium. At equilibrium, the concentrations of reactants and products remain constant over time because their rates are balanced.
If you consider a generic reaction involving substances A and B producing substances C and D, it can be expressed as: refers to the partial pressures of the substances, and and are the stoichiometric coefficients from the balanced reaction equation.
It is important to note that solids and pure liquids are not included in the equilibrium constant expression. The chemical equilibrium is dynamic because, even though the concentrations of products and reactants remain constant, the reactions continue to occur at the molecular level.
If you consider a generic reaction involving substances A and B producing substances C and D, it can be expressed as:
- A + B ⇌ C + D
It is important to note that solids and pure liquids are not included in the equilibrium constant expression. The chemical equilibrium is dynamic because, even though the concentrations of products and reactants remain constant, the reactions continue to occur at the molecular level.
Thermodynamics
Thermodynamics in chemical reactions involves the study of energy changes that occur during a chemical reaction. One key aspect of thermodynamics related to chemical equilibrium is the concept of Gibbs free energy, . Gibbs free energy determines the spontaneity of a reaction. When is negative, the process is spontaneous, indicating that the forward reaction is favored. is the universal gas constant, and is the temperature in Kelvin. Understanding this relationship helps infer how changes in temperature can shift the position of equilibrium.
Furthermore, Le Chatelier's Principle provides insight into how a system at equilibrium responds to external changes. According to this principle, if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the system will adjust itself to counteract that change and establish a new equilibrium position. This principle is an essential part of thermodynamics and applies to various chemical processes.
- If
, the reaction is non-spontaneous in the forward direction. - If
, the system is at equilibrium.
Furthermore, Le Chatelier's Principle provides insight into how a system at equilibrium responds to external changes. According to this principle, if a system at equilibrium is subjected to a change in concentration, pressure, or temperature, the system will adjust itself to counteract that change and establish a new equilibrium position. This principle is an essential part of thermodynamics and applies to various chemical processes.
Reaction Equations
Reaction equations are symbolic representations of chemical reactions. They illustrate how reactants are transformed into products. A balanced reaction equation has equal numbers of each atom on both sides of the equation, maintaining the principle of the conservation of mass.
Consider the equation from the problem:
Balancing is crucial because it ensures matter is neither created nor destroyed, only transformed. Coefficients are used in front of compounds to balance the equation, not by altering subscripts in the compounds themselves.
Reaction equations also aid in deriving equilibrium constant expressions. They provide the stoichiometric coefficients, which serve as exponents in the expression for . Thus, understanding how to write and balance reaction equations is fundamental in calculating equilibrium constants and analyzing chemical reactions.
Consider the equation from the problem:
Balancing is crucial because it ensures matter is neither created nor destroyed, only transformed. Coefficients are used in front of compounds to balance the equation, not by altering subscripts in the compounds themselves.
Reaction equations also aid in deriving equilibrium constant expressions. They provide the stoichiometric coefficients, which serve as exponents in the expression for