The expression for equilibrium constant, `K_(c)` for the following reaction is
`2Cu(NO_(3))_(2(s))hArr2CuO_((s))+4NO_(2(g))+O_(2(g))`

Options

A. `K_(c)=([CuO_((s))]^(2)[NO_(2(g))]^(4)[O_(2(g))])/([Cu(NO_(3))_(2(s))]^(2))`
B. `K_(c)=([NO_(2(g))]^(4)[O_(2(g))])/([Cu(NO_(3))_(2(g))]^(2))`
C. `K_(c)=[NO_(2(g))]^(4)[O_(2(g))]`
D. `K_(c)=([CuO_((s))]^(2))/([Cu(NO_(3))_(2(g))]^(2))`

Explanation

To derive the expression for the equilibrium constant \( K_c \) for the reaction:

\[ 2 \text{Cu(NO}_3\text{)}_2(s) \rightleftharpoons 2 \text{CuO}(s) + 4 \text{NO}_2(g) + \text{O}_2(g) \]

we follow these steps:

### Step 1: Identify the states of the reactants and products
In the given reaction, we have:
- Reactants: \( 2 \text{Cu(NO}_3\text{)}_2 \) (solid)
- Products: \( 2 \text{CuO} \) (solid), \( 4 \text{NO}_2 \) (gas), and \( \text{O}_2 \) (gas)

### Step 2: Understand the concept of equilibrium constant \( K_c \)
The equilibrium constant \( K_c \) is defined in terms of the concentrations of the products and reactants at equilibrium. It is expressed as:

\[ K_c = \frac{[\text{Products}]}{[\text{Reactants}]} \]

### Step 3: Exclude solids from the expression
In the case of heterogeneous equilibria, only the concentrations of gaseous and aqueous species are included in the expression for \( K_c \). The concentrations of pure solids and pure liquids are not included because their activities are defined as 1.

### Step 4: Write the expression for \( K_c \)
From the reaction, the gaseous products are \( \text{NO}_2 \) and \( \text{O}_2 \). The expression for \( K_c \) will only include these gaseous components:

\[ K_c = \frac{[\text{NO}_2]^4 [\text{O}_2]^1}{[\text{Cu(NO}_3\text{)}_2]^0 [\text{CuO}]^0} \]

Since the concentrations of solids are not included, we can simplify this to:

\[ K_c = [\text{NO}_2]^4 [\text{O}_2]^1 \]

### Final Expression
Thus, the final expression for the equilibrium constant \( K_c \) for the given reaction is:

\[ K_c = [\text{NO}_2]^4 [\text{O}_2] \]