To identify the correct equilibrium constant expression for the given reaction
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g) \leftrightarrow 6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(g), \][/tex]
it is essential to remember some fundamental points about equilibrium constants:
1. The concentration of solids (denoted by [tex]\((s)\)[/tex]) is not included in the expression for the equilibrium constant.
2. For gases (denoted by [tex]\((g)\)[/tex]), their concentrations (or partial pressures) are included in the expression.
The general form of the equilibrium constant expression for a reaction [tex]\( a \text{A} + b \text{B} \leftrightarrow c \text{C} + d \text{D} \)[/tex] is:
[tex]\[ K_{eq} = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}. \][/tex]
Applying this to our specific reaction:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + 6 \text{O}_2(g) \leftrightarrow 6 \text{CO}_2(g) + 6 \text{H}_2\text{O}(g), \][/tex]
we need to include the gaseous substances but exclude the solid glucose ([tex]\(\text{C}_6\text{H}_{12}\text{O}_6\)[/tex]).
Thus, the correct equilibrium constant expression is:
[tex]\[ K_{eq} = \frac{[\text{CO}_2]^6 [\text{H}_2\text{O}]^6}{[\text{O}_2]^6}. \][/tex]
This matches none of the options directly given. However, it appears that the last extra option 'DONE [tex]$\checkmark$[/tex]' asserts some incompleteness or error in the provided options, clarifying that these options might not directly cover the correct answer. So, this step-by-step methodological derivation gives the expression you need.
To finalize, the correct equilibrium constant expression for the given reaction is:
[tex]\[ K_{eq} = \frac{[\text{CO}_2]^6 [\text{H}_2\text{O}]^6}{[\text{O}_2]^6}. \][/tex]
