For the following reaction in gaseous phase `CO(g)+1/2O_(2) rarr CO_(2) K_(P)/K_(c)` is

Options

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

Explanation

To solve the problem of finding the ratio \( \frac{K_p}{K_c} \) for the reaction \( \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \), we will follow these steps:

### Step 1: Write the reaction
The reaction given is:
\[ \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{CO}_2(g) \]

### Step 2: Identify the number of moles of gases
Next, we need to determine the number of moles of gaseous products and reactants:
- **Products**:
- 1 mole of \( \text{CO}_2 \)

- **Reactants**:
- 1 mole of \( \text{CO} \)
- \( \frac{1}{2} \) mole of \( \text{O}_2 \)

Total moles of reactants = \( 1 + \frac{1}{2} = \frac{3}{2} \)

### Step 3: Calculate \( \Delta N_g \)
Now we calculate \( \Delta N_g \):
\[ \Delta N_g = \text{(moles of products)} - \text{(moles of reactants)} = 1 - \frac{3}{2} = 1 - 1.5 = -\frac{1}{2} \]

### Step 4: Use the relationship between \( K_p \) and \( K_c \)
The relationship between \( K_p \) and \( K_c \) is given by:
\[ K_p = K_c (R T)^{\Delta N_g} \]
Substituting \( \Delta N_g \):
\[ K_p = K_c (R T)^{-\frac{1}{2}} \]

### Step 5: Find \( \frac{K_p}{K_c} \)
To find \( \frac{K_p}{K_c} \):
\[ \frac{K_p}{K_c} = (R T)^{-\frac{1}{2}} \]

### Final Answer
Thus, the ratio \( \frac{K_p}{K_c} \) is:
\[ \frac{K_p}{K_c} = \frac{1}{\sqrt{R T}} \]