Problem 23
Question
When this reaction comes to equilibrium, will the concentrations of the reactants or peoducts be greater? Does the answer to this question depend on the initial concentrations of the reac. tants and products? MISSED THIST Read Section 16.3; Watch KCV 16.3 $$ A(s)+B(s)=2 C(g) K_{c}-1.4 \times 10^{-5} $$
Step-by-Step Solution
Verified Answer
At equilibrium, the concentrations of the reactants (solids) will be greater due to the small value of Kc, \(1.4 \times 10^{-5}\). The answer does not depend on the initial concentrations of the reactants since they are solids.
1Step 1: Identify the Equation
Firstly, identify the balanced chemical equation for the reaction and note the state of each component: reactants A(s) and B(s) are solids, and the product C(g) is a gas.
2Step 2: Understand the Reaction Quotient and Equilibrium Constant
For the reaction at equilibrium, the concentrations of the solid reactants A and B do not appear in the expression for the equilibrium constant, since their concentrations are constant. We focus on the concentration of the gaseous product C when determining the equilibrium state.
3Step 3: Analyze the Magnitude of Kc
Examine the equilibrium constant, Kc, which has a value of \(1.4 \times 10^{-5}\). A small value of Kc implies that the equilibrium favors the reactants, and the concentrations of the reactants will be greater than the concentrations of the products at equilibrium.
4Step 4: Evaluate the Initial Concentrations
The equilibrium concentrations of C(g) do not depend on the initial concentrations of the solids A and B because solids are not included in the equilibrium expression.
Key Concepts
Equilibrium ConstantReaction QuotientBalanced Chemical Equation
Equilibrium Constant
Understanding the equilibrium constant, denoted as \( K_c \), is integral to mastering chemical equilibria. The equilibrium constant is a numerical value that provides essential information about the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction. When a reaction has reached equilibrium, the reactants and products are present at certain concentrations that do not change over time.
For the reaction \( A(s) + B(s) \leftrightarrow 2C(g) \), with \( K_c = 1.4 \times 10^{-5} \), the equilibrium constant indicates the tendency of the reaction to lean towards the formation of reactants or products. With a smaller \( K_c \), such as in our example, the reaction favors the formation of the reactants. This means that, at equilibrium, the concentration of the solid reactants \( A \) and \( B \) will be higher than that of the gaseous products \( C \).
It is important to remember that \( K_c \) only includes the concentrations of the substances in the gaseous and aqueous states. Solids and pure liquids have fixed concentrations and, therefore, are not included in the calculation of \( K_c \). This principle clarifies why solid reactants are omitted in the calculation for our example reaction.
For the reaction \( A(s) + B(s) \leftrightarrow 2C(g) \), with \( K_c = 1.4 \times 10^{-5} \), the equilibrium constant indicates the tendency of the reaction to lean towards the formation of reactants or products. With a smaller \( K_c \), such as in our example, the reaction favors the formation of the reactants. This means that, at equilibrium, the concentration of the solid reactants \( A \) and \( B \) will be higher than that of the gaseous products \( C \).
It is important to remember that \( K_c \) only includes the concentrations of the substances in the gaseous and aqueous states. Solids and pure liquids have fixed concentrations and, therefore, are not included in the calculation of \( K_c \). This principle clarifies why solid reactants are omitted in the calculation for our example reaction.
Reaction Quotient
The reaction quotient, \( Q \), serves as a predictive tool in determining the direction in which a reaction will shift to reach equilibrium. It is calculated in the same way as the equilibrium constant, using the initial concentrations of the reactants and products before equilibrium is achieved.
In practice, you find the value of \( Q \) by plugging the initial concentrations into the equilibrium expression. If \( Q < K_c \), the reaction will proceed in the forward direction, converting reactants into products, until equilibrium is reached. Conversely, if \( Q > K_c \), the reaction will proceed in the reverse direction to restore balance. When \( Q = K_c \), the system is already at equilibrium, and no shift is needed.
For the given reaction, since the reactants are solids and do not appear in the equilibrium expression, \( Q \) will depend on the initial concentration of \( C(g) \). By comparing \( Q \) and the given \( K_c \), you can predict the direction of change. However, regardless of the initial concentration of \( C(g) \), the small value of \( K_c \) suggests that the products' concentration will decrease over time if the reaction started with high levels of \( C(g) \).
In practice, you find the value of \( Q \) by plugging the initial concentrations into the equilibrium expression. If \( Q < K_c \), the reaction will proceed in the forward direction, converting reactants into products, until equilibrium is reached. Conversely, if \( Q > K_c \), the reaction will proceed in the reverse direction to restore balance. When \( Q = K_c \), the system is already at equilibrium, and no shift is needed.
For the given reaction, since the reactants are solids and do not appear in the equilibrium expression, \( Q \) will depend on the initial concentration of \( C(g) \). By comparing \( Q \) and the given \( K_c \), you can predict the direction of change. However, regardless of the initial concentration of \( C(g) \), the small value of \( K_c \) suggests that the products' concentration will decrease over time if the reaction started with high levels of \( C(g) \).
Balanced Chemical Equation
A balanced chemical equation is a representation of a chemical reaction in which the number of atoms for each element, and the total charge, are the same on both the reactant and product sides of the equation. This balance is a law of nature, reflecting the principle of the conservation of matter.
For the example reaction \( A(s) + B(s) \rightarrow 2C(g) \), the balancing coefficients indicate that one mole of \( A \) reacts with one mole of \( B \) to produce two moles of \( C \). Balancing is crucial as it ensures that the law of conservation of mass is obeyed and provides a clear stoichiometric relationship between the reactants and products, which is used to determine the equilibrium constant and reaction quotient.
A well-balanced equation like this one provides a framework for understanding the stoichiometry of the reaction, which in turn allows us to correctly set up the equilibrium expression and calculate the equilibrium constant, \( K_c \), and the reaction quotient, \( Q \). Additionally, in the context of our problem, noting that solid reactants A and B do not appear in the expression for \( K_c \) is a direct consequence of having a balanced equation.
For the example reaction \( A(s) + B(s) \rightarrow 2C(g) \), the balancing coefficients indicate that one mole of \( A \) reacts with one mole of \( B \) to produce two moles of \( C \). Balancing is crucial as it ensures that the law of conservation of mass is obeyed and provides a clear stoichiometric relationship between the reactants and products, which is used to determine the equilibrium constant and reaction quotient.
A well-balanced equation like this one provides a framework for understanding the stoichiometry of the reaction, which in turn allows us to correctly set up the equilibrium expression and calculate the equilibrium constant, \( K_c \), and the reaction quotient, \( Q \). Additionally, in the context of our problem, noting that solid reactants A and B do not appear in the expression for \( K_c \) is a direct consequence of having a balanced equation.
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