To determine the equilibrium expression for the given reaction:
[tex]\[ C ( s ) + O _2( g ) \rightleftarrows CO _2( g ) \][/tex]
First, note that the equilibrium constant expression ([tex]\(K_c\)[/tex]) for a general reaction:
[tex]\[ aA + bB \rightleftharpoons cC + dD \][/tex]
is given by:
[tex]\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \][/tex]
However, according to the principles of equilibrium expressions, the concentrations of pure solids and pure liquids do not appear in the expression. This is because their activity is constant and does not change during the course of the reaction.
In the given reaction:
[tex]\[ C ( s ) + O_2 ( g ) \rightleftarrows CO_2 ( g ) \][/tex]
- [tex]\(C\)[/tex] is a solid.
- [tex]\(O_2\)[/tex] is a gas.
- [tex]\(CO_2\)[/tex] is a gas.
Since [tex]\(C\)[/tex] is a solid, it is not included in the equilibrium expression. Therefore, we only consider the gases, [tex]\(O_2\)[/tex] and [tex]\(CO_2\)[/tex].
The equilibrium expression for the reaction involves only the concentrations of the gases:
[tex]\[ K_c = \frac{[CO_2]}{[O_2]} \][/tex]
Thus, the correct option is:
A. [tex]\(\frac{\left[ CO _2\right]}{\left[ O _2\right]}\)[/tex]
