The equilibrium constant for the reaction `Zn(s)+CO_(2)(g)hArrZnO(s)+CO(g)` is

Options

A. `(P_(CO))/(P_(CO_(2)))`
B. `([ZnO])/([Zn])`
C. `(P_(ZnO)P_(CO))/(P_(Zn)P_(CO_(2)))`
D. `(P_(Zn)P_(CO_(2)))/(P_(ZnO)P_(CO_(2)))`

Answer

To find the equilibrium constant \( K \) for the reaction

\[ \text{Zn(s)} + \text{CO}_2(g) \rightleftharpoons \text{ZnO(s)} + \text{CO(g)} \]

we will follow these steps:

### Step 1: Identify the components of the reaction
The given reaction involves:
- Reactants: Zinc (Zn) in solid form and Carbon Dioxide (CO₂) in gaseous form.
- Products: Zinc Oxide (ZnO) in solid form and Carbon Monoxide (CO) in gaseous form.

### Step 2: Write the expression for the equilibrium constant
The equilibrium constant \( K \) is defined in terms of the concentrations (or partial pressures) of the products and reactants. The general formula for the equilibrium constant \( K \) for a reaction

\[ aA + bB \rightleftharpoons cC + dD \]

is given by:

\[ K = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

### Step 3: Apply the expression to the given reaction
For our reaction, we note that:
- The solid states (Zn and ZnO) do not appear in the equilibrium expression because their activities are considered to be 1.
- We only consider the gases (CO₂ and CO).

Thus, the equilibrium constant \( K \) for the reaction can be expressed as:

\[ K = \frac{P_{\text{CO}}}{P_{\text{CO}_2}} \]

where \( P_{\text{CO}} \) is the partial pressure of carbon monoxide and \( P_{\text{CO}_2} \) is the partial pressure of carbon dioxide.

### Step 4: Final expression for the equilibrium constant
The final expression for the equilibrium constant for the reaction is:

\[ K = \frac{P_{\text{CO}}}{P_{\text{CO}_2}} \]

### Summary
The equilibrium constant for the reaction \( \text{Zn(s)} + \text{CO}_2(g) \rightleftharpoons \text{ZnO(s)} + \text{CO(g)} \) is given by:

\[ K = \frac{P_{\text{CO}}}{P_{\text{CO}_2}} \]