At high temperature, the following reaction occurs
`4CuO(s)hArr 2Cu_(2)O(s)+O_(2)(g)`
Consider the following statements regarding reaction
1. `K_(p)=P_(O_(2))`
2. `K_(p)` depends upon the amounts of `CuO and Cu_(2)O`
3. `K_(p) lt lt K_(c)`
4. `K_(p) gt K_(c)`
Of the statements

Options

A. 1 and 2 are correct
B. 1, 2 and 3 are correct
C. 1 and 4 are correct
D. 2 and 3 are correct

Answer

To solve the problem regarding the equilibrium constant \( K_p \) for the reaction:

\[ 4 \text{CuO}(s) \rightleftharpoons 2 \text{Cu}_2\text{O}(s) + \text{O}_2(g) \]

we will analyze each statement provided.

### Step 1: Analyze Statement 1
**Statement 1:** \( K_p = P_{O_2} \)

In this reaction, the only gaseous product is \( O_2 \). The equilibrium constant \( K_p \) is defined in terms of the partial pressures of the gaseous products. Since the solids do not contribute to the equilibrium expression, we have:

\[ K_p = P_{O_2} \]

**Conclusion:** This statement is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** \( K_p \) depends upon the amounts of \( \text{CuO} \) and \( \text{Cu}_2\text{O} \)

The equilibrium constant \( K_p \) only depends on the concentrations (or partial pressures) of the gaseous products and not on the amounts of solids. Therefore, the amounts of \( \text{CuO} \) and \( \text{Cu}_2\text{O} \) do not affect \( K_p \).

**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze Statement 3
**Statement 3:** \( K_p \ll K_c \)

To determine the relationship between \( K_p \) and \( K_c \), we use the equation:

\[ K_p = K_c (RT)^{\Delta n} \]

where \( \Delta n \) is the change in the number of moles of gas (moles of products - moles of reactants). In this case:

- Moles of gaseous products = 1 (from \( O_2 \))
- Moles of gaseous reactants = 0

Thus, \( \Delta n = 1 - 0 = 1 \).

Therefore, we have:

\[ K_p = K_c (RT)^{1} \]

Since \( R \) and \( T \) are both positive quantities, it follows that:

\[ K_p > K_c \]

**Conclusion:** This statement is **incorrect**.

### Step 4: Analyze Statement 4
**Statement 4:** \( K_p > K_c \)

From our analysis in Step 3, we concluded that:

\[ K_p = K_c (RT)^{1} \]

Since \( R \) and \( T \) are positive, \( K_p \) is indeed greater than \( K_c \).

**Conclusion:** This statement is **correct**.

### Final Summary of Statements
- **Statement 1:** Correct
- **Statement 2:** Incorrect
- **Statement 3:** Incorrect
- **Statement 4:** Correct

Thus, the correct statements are 1 and 4.