For the reaction `CO(g) + 0.5O_(2)(g) rarr CO_(2)(g) K_(P)//K_(c)` is equal to

Options

A. `sqrt(RT)`
B. `1/sqrt(RT)`
C. 1
D. `RT^(2)`

Explanation

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

\[ \text{CO(g)} + 0.5 \text{O}_2(g) \rightleftharpoons \text{CO}_2(g) \]

we will follow these steps:

### Step 1: Write the expression for \( K_p \) and \( K_c \)

The equilibrium constant \( K_c \) is expressed in terms of molar concentrations, while \( K_p \) is expressed in terms of partial pressures. For the given reaction, we can write:

\[ K_c = \frac{[\text{CO}_2]}{[\text{CO}][\text{O}_2]^{0.5}} \]

\[ K_p = \frac{P_{\text{CO}_2}}{P_{\text{CO}} \cdot P_{\text{O}_2}^{0.5}} \]

### Step 2: Determine \( \Delta n_g \)

The change in the number of moles of gas, \( \Delta n_g \), is calculated as:

\[ \Delta n_g = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]

From the reaction, we see:

- Products: 1 mole of \( \text{CO}_2 \)
- Reactants: 1 mole of \( \text{CO} \) + 0.5 moles of \( \text{O}_2 \) = 1.5 moles

Thus,

\[ \Delta n_g = 1 - 1.5 = -0.5 \]

### Step 3: Use the relationship between \( K_p \) and \( K_c \)

The relationship between \( K_p \) and \( K_c \) is given by the formula:

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

Substituting \( \Delta n_g \):

\[ K_p = K_c \cdot (RT)^{-0.5} \]

### Step 4: Find \( \frac{K_p}{K_c} \)

To find \( \frac{K_p}{K_c} \), we rearrange the equation:

\[ \frac{K_p}{K_c} = (RT)^{-0.5} = \frac{1}{\sqrt{RT}} \]

### Final Answer

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

\[ \frac{K_p}{K_c} = \frac{1}{\sqrt{RT}} \]