What is [tex]$K_{\text {eq }}$[/tex] for the reaction [tex]$N _2+3 H _2 \rightleftharpoons 2 NH _3$[/tex] if the equilibrium concentrations are [tex]$\left[ NH _{-}\right]=3 M[/tex], [tex]$\left[ N _{-}\right]=2 M$[/tex], and [tex]$\left[ H _{-}\right]=1 M$[/tex]?
A. [tex]$K_{ eq }=1.5$[/tex]
B. [tex]$K_{\text {eq }}=4.5$[/tex]
C. [tex]$K_{\text {eq }}=0.75$[/tex]
D. [tex]$K_{\text {eq }}=1.125$[/tex]
Answer (2)
Define the equilibrium constant expression: K e q = [ N 2 ] [ H 2 ] 3 [ N H 3 ] 2 .
Substitute the given concentrations: K e q = ( 2 ) ( 1 ) 3 ( 3 ) 2 .
Calculate the value: K e q = 2 9 = 4.5 .
The equilibrium constant is: 4.5 .
Explanation
Problem Analysis We are given the reaction N 2 + 3 H 2 ⇌ 2 N H 3 and the equilibrium concentrations [ N H 3 ] = 3 M , [ N 2 ] = 2 M , and [ H 2 ] = 1 M . We need to calculate the equilibrium constant K e q .
Defining Equilibrium Constant The equilibrium constant K e q is defined as the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their stoichiometric coefficients. For the given reaction, the expression for K e q is: K e q = [ N 2 ] [ H 2 ] 3 [ N H 3 ] 2
Substituting Values Now, we substitute the given equilibrium concentrations into the expression for K e q : K e q = ( 2 ) ( 1 ) 3 ( 3 ) 2 = 2 9
Calculating Keq Calculating the value of K e q : K e q = 2 9 = 4.5
Final Answer Therefore, the equilibrium constant K e q for the reaction is 4.5.
Examples
Understanding equilibrium constants is crucial in many real-world applications. For example, in the Haber-Bosch process, which is used to produce ammonia for fertilizers, knowing the K e q allows engineers to optimize the reaction conditions (temperature, pressure, and reactant concentrations) to maximize ammonia production. This ensures efficient fertilizer production, which is vital for global food security. Similarly, in environmental science, K e q values help predict the distribution of pollutants in different environmental compartments (air, water, soil) and assess their potential impact on ecosystems.
The equilibrium constant K e q for the reaction N 2 + 3 H 2 ⇌ 2 N H 3 is calculated using the concentrations of the products and reactants. Substituting the given values results in K e q = 4.5 . Therefore, the correct answer is option B, K e q = 4.5 .
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