To find the equilibrium expression for the given reaction:
[tex]\[ C(s) + O_2(g) \rightleftarrows CO_2(g) \][/tex]
we need to follow these steps:
1. Identify the phase of each species:
- [tex]\( C \)[/tex] is a solid (s).
- [tex]\( O_2 \)[/tex] is a gas (g).
- [tex]\( CO_2 \)[/tex] is a gas (g).
2. Write the general form of the equilibrium constant expression:
The equilibrium constant expression ([tex]\( K_c \)[/tex] for concentrations) for a reaction:
[tex]\[ aA + bB \rightleftarrows cC + dD \][/tex]
is given by:
[tex]\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \][/tex]
where:
- [A], [B], [C], and [D] are the molar concentrations of the reactants and products.
- The exponents [tex]\( a \)[/tex], [tex]\( b \)[/tex], [tex]\( c \)[/tex], and [tex]\( d \)[/tex] are the stoichiometric coefficients from the balanced chemical equation.
3. Simplify the expression considering the phases:
In the equilibrium expression, the concentration terms for solids and pure liquids are not included because their concentrations do not change during the reaction. They are considered to be constant and part of the equilibrium constant itself.
Therefore, for the given reaction:
[tex]\[ C(s) + O_2(g) \rightleftarrows CO_2(g) \][/tex]
The solid carbon ([tex]\( C \)[/tex]) is not included in the expression. Thus, the equilibrium constant expression only includes the gaseous species.
4. Write the simplified equilibrium expression:
The simplified equilibrium expression is:
[tex]\[ K_c = \frac{[CO_2]}{[O_2]} \][/tex]
Given the multiple-choice options:
A. [tex]\(\frac{[CO_2]}{[O_2][C]}\)[/tex] - Incorrect, as it includes the concentration of solid [tex]\( C \)[/tex].
B. [tex]\(\frac{[O_2][C]}{[CO_2]}\)[/tex] - Incorrect, as it includes the concentration of solid [tex]\( C \)[/tex].
C. [tex]\(\frac{[CO_2]}{[O_2]}\)[/tex] - Correct, as this is the correct simplified expression.
D. [tex]\(\frac{1}{[C]}\)[/tex] - Incorrect, as it only includes the concentration of solid [tex]\( C \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{\text{C}} \][/tex]
