To solve for the equilibrium constant expression for the given chemical reaction:
[tex]\[ \text{Fe}_2\text{O}_3(s) + 3\text{H}_2(g) \leftrightharpoons 2\text{Fe}(s) + 3\text{H}_2\text{O}(g) \][/tex]
we follow several steps.
### Step 1: Identify the Reaction Components
List all the species involved in the reaction:
- Reactants: Fe[tex]\(_2\)[/tex]O[tex]\(_3\)[/tex] (solid) and H[tex]\(_2\)[/tex] (gas)
- Products: Fe (solid) and H[tex]\(_2\)[/tex]O (gas)
### Step 2: Understand Equilibrium Constants
Equilibrium constant expressions (K[tex]\(_c\)[/tex]) are written based on the concentrations of the reactants and products at equilibrium. For gaseous and aqueous species, their concentrations (molarity) are used. Solids and pure liquids are not included in the expression since their concentrations are constant.
### Step 3: Write the Equilibrium Constant Expression
For the reaction:
[tex]\[ \text{Fe}_2\text{O}_3(s) + 3\text{H}_2(g) \leftrightharpoons 2\text{Fe}(s) + 3\text{H}_2\text{O}(g) \][/tex]
The equilibrium constant expression (K[tex]\(_c\)[/tex]) includes only the gaseous species (H[tex]\(_2\)[/tex] and H[tex]\(_2\)[/tex]O):
[tex]\[ K_c = \frac{[\text{H}_2\text{O}]^3}{[\text{H}_2]^3} \][/tex]
This expression reflects the equilibrium conditions for this specific reaction by utilizing the concentrations of the gaseous water (H[tex]\(_2\)[/tex]O) and hydrogen (H[tex]\(_2\)[/tex]) raised to the power of their coefficients in the balanced chemical equation.
### Step 4: Confirm the Form of K[tex]\(_c\)[/tex]
We can verify our expression by referring to the balanced chemical equation and ensuring only the appropriate reactants and products are included:
- Numerator: The concentration of the product H[tex]\(_2\)[/tex]O raised to the power of its coefficient from the balanced reaction (3).
- Denominator: The concentration of the reactant H[tex]\(_2\)[/tex] raised to the power of its coefficient from the balanced reaction (3).
### Final Equilibrium Expression
Thus, the equilibrium constant expression for the reaction:
[tex]\[ \text{Fe}_2\text{O}_3(s) + 3\text{H}_2(g) \leftrightharpoons 2\text{Fe}(s) + 3\text{H}_2\text{O}(g) \][/tex]
is:
[tex]\[ K_c = \frac{[\text{H}_2\text{O}]^3}{[\text{H}_2]^3} \][/tex]
This is the required equilibrium constant expression, showing the ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients from the balanced chemical equation.
