To determine the correct equilibrium constant expression for the given reaction:
[tex]\[
C (s) + O_2 (g) \leftrightarrow CO_2 (g)
\][/tex]
we need to understand a few key principles regarding equilibrium expressions.
The general form of the equilibrium constant expression for a reaction:
[tex]\[
aA + bB \leftrightarrow cC + dD
\][/tex]
is given by:
[tex]\[
K_{eq} = \frac{[C]^c [D]^d}{[A]^a [B]^b}
\][/tex]
In this expression, the concentrations of the products are in the numerator and the concentrations of the reactants are in the denominator, each raised to the power of their respective coefficients from the balanced chemical equation.
However, when dealing with equilibrium expressions involving solids and liquids:
- The concentration of a pure solid or liquid is considered to be constant and is not included in the equilibrium expression.
Given the reaction:
[tex]\[
C (s) + O_2 (g) \leftrightarrow CO_2 (g)
\][/tex]
- Carbon ([tex]\(C\)[/tex]) is a solid, so its concentration does not appear in the equilibrium expression.
- Oxygen ([tex]\(O_2\)[/tex]) is a gas and carbon dioxide ([tex]\(CO_2\)[/tex]) is also a gas. Both will be included in the equilibrium expression.
Therefore, the equilibrium constant expression for the reaction simplifies to:
[tex]\[
K_{eq} = \frac{[CO_2]}{[O_2]}
\][/tex]
Thus, the correct equilibrium constant expression for the given system is:
[tex]\[
K_{\text{eq}} = \frac{\left[ CO_2 \right]}{\left[ O_2 \right]}
\][/tex]
