Consider the reaction below.
[tex]PCl_5(g) \longleftrightarrow PCl_3(g)+Cl_2(g)[/tex]
At 500 K, the reaction is at equilibrium with the following concentrations.
[tex]
\begin{array}{l}
\left.PCl_5\right]=0.0095 M \\
\left.PCl_3\right]=0.020 \\
\left.Cl_2\right]=0.020 M
\end{array}
[/tex]
What is the equilibrium constant for the given reaction?
Answer (2)
Write the expression for the equilibrium constant: K c = [ PC l 5 ] [ PC l 3 ] [ C l 2 ] .
Substitute the given concentrations: K c = 0.0095 ( 0.020 ) ( 0.020 ) .
Calculate the equilibrium constant: K c = 0.042105263157894736 .
The equilibrium constant for the given reaction is approximately 0.042 .
Explanation
Problem Analysis The problem provides the equilibrium concentrations for the reaction: PC l 5 ( g ) ⟷ PC l 3 ( g ) + C l 2 ( g ) . We are given [ PC l 5 ] = 0.0095 M , [ PC l 3 ] = 0.020 M , and [ C l 2 ] = 0.020 M . Our goal is to calculate the equilibrium constant, K c , for this reaction.
Equilibrium Constant Expression The equilibrium constant, K c , is defined as the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants, each raised to the power of their stoichiometric coefficients. For the given reaction, the expression for K c is: K c = [ PC l 5 ] [ PC l 3 ] [ C l 2 ] .
Substitution of Concentrations Now, we substitute the given equilibrium concentrations into the expression for K c : K c = 0.0095 ( 0.020 ) ( 0.020 ) .
Calculation of K_c Calculating the value of K c : K c = 0.0095 0.0004 = 0.042105263157894736 .
Final Answer Comparing the calculated value with the given options, we see that K c ≈ 0.042 .
Examples
Understanding equilibrium constants is crucial in many real-world applications. For instance, in the production of ammonia via the Haber-Bosch process, chemists use equilibrium constants to optimize reaction conditions (temperature, pressure, and reactant ratios) to maximize ammonia yield. Similarly, in environmental science, equilibrium constants help predict the distribution of pollutants in different environmental compartments (air, water, soil), aiding in risk assessment and remediation strategies. In pharmacology, drug-receptor binding affinities are often expressed as equilibrium constants, which guide drug design and dosage optimization.
The equilibrium constant for the reaction PC l 5 ( g ) ⟷ PC l 3 ( g ) + C l 2 ( g ) can be calculated using the concentrations of the reactants and products. Substituting the given values into the equilibrium expression gives K c ≈ 0.042 . Therefore, the equilibrium constant is approximately 0.042.
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