Read the following paragraph and answer the questions given below ,
Stable equilibrium is of various type . Mechanical equilibrium is achieved when all particles are at rest and total potential energy of the system is minimum . At any stage where particles are at rest but the system is not at stabel equilibrium as it can reduce its potential energy by reverting to another position, is called metastable equilibrium . Thermal equilibrium is result from the absence of temperature gradients in the system. chemical equilibrium is obtained when no further reaction occurs between reacting substances, i.e forward and reverse rates of reaction are equal. when steam with solid iron at high temperature `Fe_3O_4(s)` and hydrogen gas are produced . But the reaction never goes to completion. this is because as the products are formed the reaction proceeds in reverse direction and when rate of reverse reaction is equal to rate of forward reaction , the concentration of reactants and products become constant and equilibrium is reached.
The correct expression for equilibrium constant of the reaction, taken as an example of chemical equilibrium in the above passage is

Options

A. `((pH_2)^2)/((pH_2O)^2)`
B. `((pH_2)^4)/((pH_2O)^4)`
C. `((pH_2)^4[Fe_3O_4])/((pH_2O)^4[Fe])`
D. `([Fe_3O_4])/([Fe])`

Answer

To find the correct expression for the equilibrium constant of the reaction described in the paragraph, we will follow these steps:

### Step 1: Identify the Reaction
From the paragraph, we know that the reaction involves steam (H₂O) reacting with solid iron (Fe) to produce solid iron(II,III) oxide (Fe₃O₄) and hydrogen gas (H₂). The balanced reaction can be written as:
\[ 3 \text{Fe} + 4 \text{H}_2\text{O} \rightleftharpoons \text{Fe}_3\text{O}_4 + 4 \text{H}_2 \]

### Step 2: Write the Expression for the Equilibrium Constant (K)
The equilibrium constant (K) for a reaction is expressed in terms of the concentrations (or partial pressures) of the products and reactants. For the reaction:
\[ K = \frac{[\text{products}]}{[\text{reactants}]} \]

### Step 3: Apply the Stoichiometry of the Reaction
From the balanced equation, we can see:
- The products are Fe₃O₄ and H₂.
- The reactants are Fe and H₂O.

The equilibrium constant expression will be:
\[ K = \frac{[\text{Fe}_3\text{O}_4][\text{H}_2]^4}{[\text{H}_2\text{O}]^4} \]

### Step 4: Consider the Physical States
Since Fe is a solid, it does not appear in the equilibrium expression. Therefore, we can simplify the expression to:
\[ K = \frac{P_{\text{H}_2}^4}{P_{\text{H}_2\text{O}}^4} \]

### Step 5: Final Expression for K
Thus, the final expression for the equilibrium constant K (or Kp if we are considering partial pressures) for the reaction is:
\[ K = \frac{P_{\text{H}_2}^4}{P_{\text{H}_2\text{O}}^4} \]

### Conclusion
The correct expression for the equilibrium constant of the reaction is:
\[ K = \frac{P_{\text{H}_2}^4}{P_{\text{H}_2\text{O}}^4} \]

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