Consider the reaction:
[tex]2 NOCl(g) \leftrightarrow 2 NO(g)+Cl_2(g)[/tex]
At equilibrium, the concentrations are as follows:
[tex]\begin{array}{l}
{[NOCl]=1.4 \cdot 10^{-2} M} \\
{[NO]=1.2: 10^{-3} M} \\
{\left[Cl_2\right]=2.2: 10^{-3} M}
\end{array}[/tex]
What is the value of [tex]K _{\text {eq }}[/tex] for the reaction expressed in scientific notation?
A. [tex]1.6 \cdot 10^{-5}[/tex]
B. [tex]6.2 \cdot 10^4[/tex]
C. [tex]1.6: 10^5[/tex]
Answer (2)
Write the expression for the equilibrium constant K e q for the given reaction: K e q = [ NOCl ] 2 [ NO ] 2 [ C l 2 ] .
Substitute the given equilibrium concentrations into the K e q expression: K e q = ( 1.4 × 1 0 − 2 ) 2 ( 1.2 × 1 0 − 3 ) 2 ( 2.2 × 1 0 − 3 ) .
Calculate the value of K e q : K e q = 1.61632653 × 1 0 − 5 .
Express the value of K e q in scientific notation: 1.6 ⋅ 1 0 − 5 .
Explanation
Problem Analysis The reaction is: 2 NOCl ( g ) ↔ 2 NO ( g ) + C l 2 ( g ) . We are given the equilibrium concentrations: [ NOCl ] = 1.4 × 1 0 − 2 M , [ NO ] = 1.2 × 1 0 − 3 M , and [ C l 2 ] = 2.2 × 1 0 − 3 M . Our goal is to calculate the equilibrium constant K e q for this reaction.
Defining the Equilibrium Constant The equilibrium constant K e q is defined as the ratio of the product of the concentrations of the products raised to their stoichiometric coefficients to the product of the concentrations of the reactants raised to their stoichiometric coefficients. For the given reaction, the expression for K e q is: K e q = [ NOCl ] 2 [ NO ] 2 [ C l 2 ]
Substituting the Values Now, we substitute the given equilibrium concentrations into the K e q expression: K e q = ( 1.4 × 1 0 − 2 ) 2 ( 1.2 × 1 0 − 3 ) 2 ( 2.2 × 1 0 − 3 )
Calculating Keq Let's calculate the value of K e q :
K e q = ( 1.4 × 1 0 − 2 ) 2 ( 1.2 × 1 0 − 3 ) 2 ( 2.2 × 1 0 − 3 ) = 1.96 × 1 0 − 4 ( 1.44 × 1 0 − 6 ) ( 2.2 × 1 0 − 3 ) = 1.96 × 1 0 − 4 3.168 × 1 0 − 9 = 1.61632653 × 1 0 − 5
Final Answer Therefore, the value of K e q for the reaction is approximately 1.6 × 1 0 − 5 .
Examples
Understanding equilibrium constants is crucial in various real-world applications. For instance, in environmental science, K e q helps predict the extent of pollutant formation in the atmosphere. In chemical engineering, it aids in optimizing reaction conditions to maximize product yield. In biochemistry, it is used to study enzyme-substrate interactions and metabolic pathways. By calculating K e q , scientists and engineers can make informed decisions to control and optimize chemical processes.
The equilibrium constant K e q for the reaction is calculated using the concentrations of the reactants and products. The value of K e q is approximately 1.6 × 1 0 − 5 . Thus, the correct option is A.
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