Kp for Lane's process is :

Options

A. `(P^(4)H_(2))/(P^(4)H_(2)O) `
B. `([Fe_(3)O_(4)])/([Fe])`
C. `(P^(4)H_(2)O)/(P^(4)H_(2))`
D. `(P^(4)H_(2))/(P^(4)H_(2)O) xx ([Fe_(3)O_(4)])/([Fe])`

Answer

To determine the expression for Kp for Lane's process, we will follow these steps:

### Step 1: Identify the Reaction
The Lane's process involves the reaction between iron and steam to produce ferrosperic oxide (Fe3O4) and hydrogen gas (H2). The balanced chemical equation for this reaction is:

\[ 3Fe + 4H_2O \rightarrow Fe_3O_4 + 4H_2 \]

### Step 2: Write the Expression for Kp
Kp is the equilibrium constant for gas-phase reactions expressed in terms of partial pressures. For the reaction, we will focus on the gaseous components, which are hydrogen (H2) and steam (H2O).

The general expression for Kp is given by:

\[ K_p = \frac{(P_{products})^{coefficients}}{(P_{reactants})^{coefficients}} \]

### Step 3: Apply the Expression to the Reaction
For our balanced reaction, the gaseous products and reactants are:

- Products: 4 moles of H2
- Reactants: 4 moles of H2O

Thus, the expression for Kp becomes:

\[ K_p = \frac{(P_{H_2})^4}{(P_{H_2O})^4} \]

### Step 4: Simplify the Expression
Since both the numerator and denominator have the same exponent (4), we can simplify the expression to:

\[ K_p = \left(\frac{P_{H_2}}{P_{H_2O}}\right)^4 \]

### Conclusion
The correct expression for Kp for Lane's process is:

\[ K_p = \frac{(P_{H_2})^4}{(P_{H_2O})^4} \]