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)
The equilibrium constant, K e q , is the ratio of products to reactants at equilibrium.
Raise the concentration of each species to the power of its stoichiometric coefficient.
For the reaction 2 S O 2 ( g ) + O 2 ( g ) ⇋ 2 S O 3 ( g ) , identify the products and reactants and their coefficients.
Write the K e q expression as K e q = [ S O 2 ] 2 [ O 2 ] [ S O 3 ] 2 .
Explanation
Understanding the Problem The problem asks us to write the equilibrium constant expression, K e q , for the given reaction: 2 S O 2 ( g ) + O 2 ( g ) ⇋ 2 S O 3 ( g ) . The equilibrium constant expression relates the concentrations of reactants and products at equilibrium.
General Form of Keq The general form of the equilibrium constant expression is given by: K e 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 chemical species at equilibrium, and the coefficients are the stoichiometric coefficients from the balanced chemical equation.
Applying to the Given Reaction For the given reaction, 2 S O 2 ( g ) + O 2 ( g ) ⇋ 2 S O 3 ( g ) , the product is S O 3 with a coefficient of 2, and the reactants are S O 2 with a coefficient of 2 and O 2 with a coefficient of 1. Therefore, the K e q expression is: K e q = [ S O 2 ] 2 [ O 2 ] [ S O 3 ] 2 This expression represents the ratio of the concentration of the product, S O 3 , raised to the power of its coefficient, to the concentrations of the reactants, S O 2 and O 2 , each raised to the power of their respective coefficients.
Final Answer Therefore, the correct K e q expression for the reaction 2 S O 2 ( g ) + O 2 ( g ) ⇋ 2 S O 3 ( g ) is: K e q = [ S O 2 ] 2 [ O 2 ] [ S O 3 ] 2
Examples
The equilibrium constant is crucial in various real-world applications, such as optimizing industrial processes. For example, in the production of sulfuric acid, the reaction 2 S O 2 ( g ) + O 2 ( g ) ⇋ 2 S O 3 ( g ) is a key step. By understanding and manipulating the equilibrium constant, chemical engineers can adjust reaction conditions (e.g., temperature, pressure, reactant concentrations) to maximize the yield of S O 3 , which is then used to produce sulfuric acid. This optimization leads to more efficient and cost-effective production.
