To determine 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 states of matter:
- Carbon (C) is a solid.
- Oxygen (O_2) is a gas.
- Carbon dioxide (CO_2) is a gas.
2. Understand the equilibrium expression:
For a general reaction:
[tex]\[ aA + bB \rightleftarrows cC + dD \][/tex]
the equilibrium expression [tex]\( K \)[/tex] is given by:
[tex]\[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \][/tex]
where the square brackets [ ] denote the concentration of the species.
3. Exclude solids and pure liquids:
In the equilibrium expression, we exclude solids and pure liquids because their activities are constant and taken as 1. In this reaction, carbon (C) is a solid and will not appear in the equilibrium expression.
4. Write the equilibrium expression:
For the reaction:
[tex]\[ C (s) + O_2 (g) \rightleftarrows CO_2 (g) \][/tex]
the equilibrium expression involves only the gases:
[tex]\[ K = \frac{[CO_2]}{[O_2]} \][/tex]
Given the choices:
A. [tex]\( \frac{[O_2] [C]}{[CO_2]} \)[/tex]
B. [tex]\( \frac{1}{[C]} \)[/tex]
C. [tex]\( \frac{[CO_2]}{[O_2] [C]} \)[/tex]
D. [tex]\( \frac{[CO_2]}{[O_2]} \)[/tex]
The correct equilibrium expression is:
[tex]\[ \frac{[CO_2]}{[O_2]} \][/tex]
Thus, the answer is :
D. [tex]\( \frac{[CO_2]}{[O_2]} \)[/tex]
