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

Options

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

Explanation

To solve the problem regarding the relationship between \( K_p \) and \( K_c \) 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 change in moles of gas (\( \Delta N_g \))

For the reaction:

- Reactants: 1 mole of CO + 0.5 moles of O2 = 1.5 moles
- Products: 1 mole of CO2

Now, we calculate \( \Delta N_g \):

\[ \Delta N_g = \text{moles of gaseous products} - \text{moles of gaseous reactants} \]
\[ \Delta N_g = 1 - 1.5 = -0.5 \]

### Step 2: Use the relationship between \( K_p \) and \( K_c \)

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

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

### Step 3: Substitute \( \Delta N_g \) into the equation

Substituting \( \Delta N_g = -0.5 \) into the equation:

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

This can also be rewritten as:

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

### Step 4: Final expression

Thus, we can express the relationship as:

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

This indicates that \( K_p \) is inversely proportional to the square root of \( RT \).

### Conclusion

The final answer is:

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