Consider the equation below.
[tex]$CaCO_3(s) \longleftrightarrow CaO(s)+CO_2(g)$[/tex]
What is the equilibrium constant expression for the given reaction?
A. [tex]$K _{ eq }=\frac{[ CaO ]}{\left[ CaCO _3\right]}$[/tex]
B. [tex]$K _{\text {eq }}=\frac{\left[ CO _2\right][ CaO ]}{\left[ CaCO _3\right]}$[/tex]
C. [tex]$K _{\text {eq }}=\left[ CO _2\right]$[/tex]
D. [tex]$K_{\text {eq }}=\frac{1}{\left[ CO _2\right]}$[/tex]
Answer (2)
The equilibrium constant expression relates the concentrations of products to reactants at equilibrium.
Solids and pure liquids are excluded from the equilibrium constant expression.
Only the concentration of C O 2 ( g ) is included in the expression.
The equilibrium constant expression is K e q = [ C O 2 ] .
Explanation
Understanding the Problem We are asked to find the equilibrium constant expression for the reaction: C a C O 3 ( s ) ⟷ C a O ( s ) + C O 2 ( g ) . The equilibrium constant expression relates the concentrations of reactants and products at equilibrium.
Key Rule The general form of the equilibrium constant expression is given by 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. However, there's a key rule to remember: solids and pure liquids do not appear in the equilibrium constant expression because their activities are defined as 1.
Applying the Rule to the Reaction In our reaction, C a C O 3 ( s ) and C a O ( s ) are solids. Therefore, their concentrations are not included in the equilibrium constant expression. Only the concentration of C O 2 ( g ) , which is a gas, will be included.
Writing the Equilibrium Constant Expression Thus, the equilibrium constant expression is simply: K e q = [ C O 2 ] .
Final Answer The correct option is K e q = [ C O 2 ] .
Examples
Understanding equilibrium constants is crucial in many real-world applications. For example, in environmental science, it helps predict the concentration of pollutants in the air or water. In chemical engineering, it's used to optimize reaction conditions for industrial processes, ensuring maximum product yield. In the context of the given reaction, it can help predict the amount of carbon dioxide released during the decomposition of calcium carbonate, which is important in understanding climate change and geological processes.
The equilibrium constant expression for the reaction C a C O 3 ( s ) ⟷ C a O ( s ) + C O 2 ( g ) is K e q = [ C O 2 ] , including only the gaseous component. Therefore, the correct answer is option C. Solids do not contribute to the equilibrium expression as their activities are taken as 1.
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