What is the equilibrium constant for the reaction $N _2(g)+ O _2(g)=2 NO (g)$?
A. $K _{ eq }=\frac{[ NO ]}{\left| N _2\right| O _2 \mid}$
B. $K _{24}=\frac{29 MOI }{ N _2\left| O _2\right|}$
C. $K_{eq}=\frac{\left( NO ^2\right.}{ N _2 IO _2 I }$
D. $K_{eq}=\frac{ xMOI ^{+}}{ N _2 \uparrow\left| O _2\right|}$
Answer (2)
The equilibrium constant K e q represents the ratio of products to reactants at equilibrium.
For the reaction N 2 ( g ) + O 2 ( g ) ⇌ 2 NO ( g ) , the general formula for K e q is applied.
Substituting the reactants and products into the K e q expression gives K e q = [ N 2 ] [ O 2 ] [ NO ] 2 .
The correct option matching this expression is C, thus the final answer is C .
Explanation
Understanding Equilibrium Constant The equilibrium constant, denoted as K e q , is a value that represents the ratio of products to reactants at equilibrium in a reversible reaction. For the given reaction: N 2 ( g ) + O 2 ( g ) i g h t h l e f t ha r p oo n s 2 NO ( g ) we need to determine the correct expression for K e q .
General Formula for Equilibrium Constant The general formula for the equilibrium constant K e q for a reversible reaction 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 For a general reaction: a A + b B i g h t h l e f t ha r p oo n sc C + d D the equilibrium constant is expressed as: K e q = [ A ] a [ B ] b [ C ] c [ D ] d where [A], [B], [C], and [D] are the equilibrium concentrations of the reactants and products, and a, b, c, and d are their respective stoichiometric coefficients.
Applying to the Given Reaction Applying this formula to the given reaction: N 2 ( g ) + O 2 ( g ) i g h t h l e f t ha r p oo n s 2 NO ( g ) Here, N 2 and O 2 are the reactants, and NO is the product. The stoichiometric coefficients are 1 for N 2 , 1 for O 2 , and 2 for NO .
Substituting into the Expression Substituting the reactants, products, and their coefficients into the K e q expression, we get: K e q = [ N 2 ] [ O 2 ] [ NO ] 2 This is because the coefficient for NO is 2, and the coefficients for N 2 and O 2 are both 1.
Identifying the Correct Option Comparing the derived expression with the given options: A. K e q = [ N 2 ] [ O 2 ] [ NO ] B. K e q = N 2 [ O 2 ] 29 MO I C. K e q = [ N 2 ] [ O 2 ] [ NO ] 2 D. K e q = N 2 ↑ [ O 2 ] x MO I + Option C matches the derived expression for K e q .
Final Answer Therefore, the correct expression for the equilibrium constant for the reaction N 2 ( g ) + O 2 ( g ) = 2 NO ( g ) is: K e q = [ N 2 ] [ O 2 ] [ NO ] 2 So, the answer is C.
Examples
The equilibrium constant is crucial in various real-world applications, such as industrial chemical production. For example, in the Haber-Bosch process, nitrogen and hydrogen react to form ammonia, a key ingredient in fertilizers. By understanding and manipulating the equilibrium constant, engineers can optimize reaction conditions (temperature, pressure, and reactant concentrations) to maximize ammonia production, making the process more efficient and cost-effective. This ensures a higher yield of ammonia, which directly impacts agricultural productivity by providing essential nutrients for plant growth.
The equilibrium constant K e q for the reaction N 2 ( g ) + O 2 ( g ) = 2 NO ( g ) is given by the expression K e q = [ N 2 ] [ O 2 ] [ NO ] 2 . This matches option C from the provided choices. Thus, the correct answer is C.
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