Given the following reaction at equilibrium, write the Keq expression.
$2 SO_2(g)+O_2(g) \leftrightharpoons 2 SO_3(g)$
A. $Keq =\frac{\left[ SO _2\right]^2\left[ O _2\right]}{\left[ SO _3\right]^2}$
B. $Keq =\frac{\left[ SO _3\right]}{\left[ SO _2\right]\left[ O _2\right]}$
C. $Keq =\frac{\left[ SO _3\right]^2}{\left[ SO _2\right]^2\left[ O _2\right]}$
D. $Keq =\frac{\left[ SO _2\right]\left[ O _2\right]}{\left[ SO _3\right]}$
Answer (1)
Identify the reactants ( S O 2 and O 2 ) and the product ( S O 3 ) in the given reaction.
Write the general form of the equilibrium constant expression: Ke q = [ R e a c t an t s ] coe ff i c i e n t s [ P ro d u c t s ] coe ff i c i e n t s .
Substitute the reactants, products, and their coefficients into the Ke q expression: Ke q = [ S O 2 ] 2 [ O 2 ] [ S O 3 ] 2 .
The correct Ke q expression is Ke q = [ S O 2 ] 2 [ O 2 ] [ S O 3 ] 2 .
Explanation
Understanding the Reaction Let's analyze the given chemical reaction and determine the correct equilibrium constant expression.
Identifying Reactants and Products The given reaction is: 2 S O 2 ( g ) + O 2 ( g ) ⇋ 2 S O 3 ( g ) In this reaction, S O 2 and O 2 are the reactants, and S O 3 is the product.
General Form of Keq The general form of the equilibrium constant expression, Ke q , is given by: Ke q = [ R e a c t an t s ] coe ff i c i e n t s [ P ro d u c t s ] coe ff i c i e n t s where the square brackets denote the molar concentrations of the species at equilibrium, and the coefficients are the stoichiometric coefficients from the balanced chemical equation.
Writing the Keq Expression For the given reaction, the Ke q expression is: Ke q = [ S O 2 ] 2 [ O 2 ] [ S O 3 ] 2 This expression has the concentration of the product S O 3 raised to the power of its coefficient (2) in the numerator, and the concentrations of the reactants S O 2 and O 2 raised to the powers of their respective coefficients (2 and 1) in the denominator.
Final Answer Comparing the derived Ke q expression with the given options, the correct expression is: Ke q = [ S O 2 ] 2 [ O 2 ] [ S O 3 ] 2 So, the third option is the correct one.
Examples
The equilibrium constant is a crucial concept in various fields, including environmental science and industrial chemistry. For instance, in environmental science, understanding the equilibrium of reactions involving pollutants like sulfur dioxide ( S O 2 ) helps in predicting and controlling air quality. In industrial chemistry, the equilibrium constant is essential for optimizing the production of chemicals such as sulfuric acid ( H 2 S O 4 ), which is produced from S O 3 . By manipulating reaction conditions to favor product formation, industries can maximize efficiency and minimize waste, leading to more sustainable and economically viable processes.
