`K_(p)//K_(c)` for the reaction
`CO(g)+1/2 O_(2)(g) hArr CO_(2)(g)` is

Options

A. `RT`
B. `(RT)^(1//2)`
C. `(1)/((RT)^(3))`
D. `(1)/sqrt(RT)`

Explanation

To find the ratio \( K_p/K_c \) for the reaction:

\[ \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightleftharpoons \text{CO}_2(g) \]

we will follow these steps:

### Step 1: Identify the reaction and write the expression for \( K_c \) and \( K_p \)

For the reaction:

\[ \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightleftharpoons \text{CO}_2(g) \]

The equilibrium constant \( K_c \) is defined as:

\[ K_c = \frac{[\text{CO}_2]}{[\text{CO}][\text{O}_2]^{1/2}} \]

And the equilibrium constant \( K_p \) is defined as:

\[ K_p = \frac{P_{\text{CO}_2}}{P_{\text{CO}} \cdot P_{\text{O}_2}^{1/2}} \]

### Step 2: Calculate \( \Delta n \)

To relate \( K_p \) and \( K_c \), we need to calculate \( \Delta n \), which is the change in the number of moles of gas:

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

In our reaction:

- Moles of gaseous products = 1 (from CO₂)
- Moles of gaseous reactants = 1 (from CO) + 0.5 (from O₂) = 1.5

Thus,

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

### Step 3: Relate \( K_p \) and \( K_c \)

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

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

Substituting \( \Delta n = -0.5 \):

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

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

Now, we can find the ratio \( \frac{K_p}{K_c} \):

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

### Final Answer

Thus, the ratio \( K_p/K_c \) for the given reaction is:

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