What is the Keq expression for the following equilibrium reaction?
$2 CO(g)+O_2(g) \leftrightharpoons 2 CO_2(g)$
A. $Keq =\frac{[ CO ]\left[ O _2\right]}{\left[ CO _2\right]}$
B. $Keq =\frac{\left[ CO ^2\left[ O _2\right]\right.}{\left[ CO _2\right]^2}$
C. $Keq =\frac{\left[ CO _2\right]^2}{[ CO ]^2\left[ O _2\right]}$
D. $Keq =\frac{\left[ CO _2\right]}{[ CO ]\left[ O _2\right]}$
Answer (2)
The equilibrium constant, K e q , is the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients.
For the general reaction a A + b B ⇋ c C + d D , the equilibrium constant is K e q = [ A ] a [ B ] b [ C ] c [ D ] d .
Applying this to 2 CO ( g ) + O 2 ( g ) ⇋ 2 C O 2 ( g ) , we identify the reactants and products and their coefficients.
The correct equilibrium constant expression is K e q = [ CO ] 2 [ O 2 ] [ C O 2 ] 2 .
Explanation
Understanding the Problem The problem asks us to determine the correct equilibrium constant expression, K e q , for the given reversible reaction: 2 CO ( g ) + O 2 ( g ) ⇋ 2 C O 2 ( g ) . The equilibrium constant is a ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients in the balanced chemical equation.
General Form of Keq For a general reversible reaction of the form: a A + b B ⇋ c C + d D where a, b, c, and d are the stoichiometric coefficients for the reactants A and B, and products C and D, respectively, the equilibrium constant, K e q , is expressed as: K e q = [ A ] a [ B ] b [ C ] c [ D ] d .
Applying to the Given Reaction Now, let's apply this general form to the given reaction: 2 CO ( g ) + O 2 ( g ) ⇋ 2 C O 2 ( g ) . Here, CO and O 2 are the reactants, and C O 2 is the product. The stoichiometric coefficient for CO is 2, for O 2 is 1, and for C O 2 is 2.
Determining the Correct Expression Substituting these values into the general K e q expression, we get: K e q = [ CO ] 2 [ O 2 ] [ C O 2 ] 2 . This expression has the concentration of the product, C O 2 , raised to the power of its coefficient (2), in the numerator, and the concentrations of the reactants, CO (raised to the power of 2) and O 2 (raised to the power of 1), in the denominator.
Final Answer Therefore, the correct K e q expression for the reaction 2 CO ( g ) + O 2 ( g ) ⇋ 2 C O 2 ( g ) is: K e q = [ CO ] 2 [ O 2 ] [ C O 2 ] 2 .
Examples
Understanding equilibrium constants is crucial in many real-world applications, such as optimizing industrial chemical processes. For example, in the production of ammonia via the Haber-Bosch process, controlling the equilibrium conditions (temperature, pressure, and reactant ratios) is essential to maximize the yield of ammonia. Similarly, in environmental science, K e q helps predict the distribution of pollutants in different environmental compartments (air, water, soil) and assess their potential impact. In biochemistry, enzyme-catalyzed reactions are often reversible and reach equilibrium, so understanding K e q is important for studying metabolic pathways and designing drugs that can modulate enzyme activity.
The equilibrium constant expression for the reaction 2 CO ( g ) + O 2 ( g ) ⇋ 2 C O 2 ( g ) is K e q = [ CO ] 2 [ O 2 ] [ C O 2 ] 2 . This expression shows the relationship between the concentrations of the products and the reactants at equilibrium. The correct choice is C.
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