Chapter 15: Problem 12
Write the expression for the equilibrium constant for the following generic chemical equation. $$ a \mathrm{~A}+b \mathrm{~B} \rightleftharpoons c \mathrm{C}+d \mathrm{D} $$
Short Answer
Expert verified
\( K = \frac{{[C]^c [D]^d}}{{[A]^a [B]^b}} \)
Step by step solution
01
Identify the Reactants and Products
Firstly, identify the reactants (A and B) and the products (C and D) in the chemical equation.
02
Write the Expression for the Equilibrium Constant
The equilibrium constant expression, denoted as K, for a given reaction is written using the concentrations of the products raised to the power of their coefficients, divided by the concentrations of the reactants raised to the power of their coefficients. In this case: \[ K = \frac{{[C]^c [D]^d}}{{[A]^a [B]^b}} \]
03
Format the Expression Properly
Ensure that the expression is formatted correctly, where the concentrations of the products C and D are raised to the power of c and d respectively, and the concentrations of the reactants A and B are raised to the power of a and b respectively.
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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 reversible reaction where the rate of the forward reaction equals the rate of the backward reaction, meaning that the concentrations of the reactants and products remain constant over time, but not necessarily equal. At equilibrium, there is no net change in the composition of the reaction mixture.
Understanding equilibrium is crucial as it indicates how far a reaction will proceed to form products under certain conditions. In the context of the provided exercise, when the chemical equation \[ aA + bB \rightleftharpoons cC + dD \] reaches equilibrium, the amounts of A, B, C, and D no longer change because the reactions in both directions are in perfect balance.
Understanding equilibrium is crucial as it indicates how far a reaction will proceed to form products under certain conditions. In the context of the provided exercise, when the chemical equation \[ aA + bB \rightleftharpoons cC + dD \] reaches equilibrium, the amounts of A, B, C, and D no longer change because the reactions in both directions are in perfect balance.
Reaction Quotient
The reaction quotient, represented as Q, is a measure that describes the relative amounts of products and reactants present during a reaction at any point in time, which can be before, at, or after reaching equilibrium. It is expressed in the same form as the equilibrium constant.
For the reaction
\[ aA + bB \rightleftharpoons cC + dD \]
the reaction quotient will be
\[ Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} \].
Comparing Q to the equilibrium constant K can predict the direction in which the reaction will proceed to reach equilibrium: if Q < K, the reaction moves forward to produce more products; if Q > K, the reaction moves backwards to produce more reactants; if Q = K, the system is at equilibrium.
For the reaction
\[ aA + bB \rightleftharpoons cC + dD \]
the reaction quotient will be
\[ Q = \frac{[C]^c[D]^d}{[A]^a[B]^b} \].
Comparing Q to the equilibrium constant K can predict the direction in which the reaction will proceed to reach equilibrium: if Q < K, the reaction moves forward to produce more products; if Q > K, the reaction moves backwards to produce more reactants; if Q = K, the system is at equilibrium.
Le Chatelier's Principle
Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, such as pressure, temperature, or concentration of components, the position of equilibrium will shift to counteract the change and re-establish equilibrium.
For instance, if we increase the concentration of reactant A in our reaction \[ aA + bB \rightleftharpoons cC + dD \], according to Le Chatelier's principle, the equilibrium will shift towards the right to decrease the concentration of A by forming more products, C and D. Similarly, if we remove some of the product D, the equilibrium will shift to the right to replace the lost D. This principle helps chemists to optimize the yield of reactions in industrial processes.
For instance, if we increase the concentration of reactant A in our reaction \[ aA + bB \rightleftharpoons cC + dD \], according to Le Chatelier's principle, the equilibrium will shift towards the right to decrease the concentration of A by forming more products, C and D. Similarly, if we remove some of the product D, the equilibrium will shift to the right to replace the lost D. This principle helps chemists to optimize the yield of reactions in industrial processes.
Concentration of Reactants and Products
The concentrations of reactants and products in a chemical reaction significantly influence the position of equilibrium and the equilibrium constant expression. In your exercise, the equilibrium constant expression is determined by the ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients.
In a closed system, any change in the concentration of the reactants or products will affect this ratio, and therefore the value of K. However, the value of K remains constant for a given reaction within a specific temperature. This property is used to predict the direction of the reaction and to calculate the concentrations of unknowns within a reaction mixture when the reaction reaches equilibrium state.
In a closed system, any change in the concentration of the reactants or products will affect this ratio, and therefore the value of K. However, the value of K remains constant for a given reaction within a specific temperature. This property is used to predict the direction of the reaction and to calculate the concentrations of unknowns within a reaction mixture when the reaction reaches equilibrium state.