For the reaction `CaCO_(3(s)) hArr CaO_((s))+CO_(2(g))k_p` is equal to

Options

A. `K_c`
B. `K_cRT`
C. `K_c(RT)^2`
D. `K_C(RT)^(-1)`

Answer

To find the relationship between \( K_p \) and \( K_c \) for the reaction:

\[ \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \]

we need to follow these steps:

### Step 1: Identify the Reaction Components
In this reaction, we have:
- Reactant: Calcium Carbonate (\( \text{CaCO}_3 \)) in solid state
- Products: Calcium Oxide (\( \text{CaO} \)) in solid state and Carbon Dioxide (\( \text{CO}_2 \)) in gaseous state

### Step 2: Write the Expression for \( K_p \)
The equilibrium constant \( K_p \) is defined in terms of the partial pressures of the gaseous products and reactants. Since \( \text{CaCO}_3 \) and \( \text{CaO} \) are solids, they do not appear in the expression. Thus, the expression for \( K_p \) is:

\[ K_p = \frac{P_{\text{CO}_2}}{1} = P_{\text{CO}_2} \]

### Step 3: Write the Expression for \( K_c \)
The equilibrium constant \( K_c \) is defined in terms of the concentrations of the products and reactants. Similarly, since solids do not appear in the expression, we have:

\[ K_c = [\text{CO}_2] \]

### Step 4: Relate \( K_p \) and \( K_c \)
The relationship between \( K_p \) and \( K_c \) is given by the formula:

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

where:
- \( R \) is the universal gas constant
- \( T \) is the temperature in Kelvin
- \( \Delta n \) is the change in the number of moles of gas, calculated as the moles of gaseous products minus the moles of gaseous reactants.

### Step 5: Calculate \( \Delta n \)
In our reaction:
- Moles of gaseous products = 1 (from \( \text{CO}_2 \))
- Moles of gaseous reactants = 0 (no gaseous reactants)

Thus,

\[ \Delta n = 1 - 0 = 1 \]

### Step 6: Substitute \( \Delta n \) into the Relationship
Now substituting \( \Delta n \) into the relationship:

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

This simplifies to:

\[ K_p = K_c RT \]

### Final Answer
Thus, the relationship between \( K_p \) and \( K_c \) for the given reaction is:

\[ K_p = K_c RT \]