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:

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

we will follow these steps:

### Step 1: Identify the Reaction and Its Components
We have the reaction:
\[ \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \rightleftharpoons \text{CO}_2(g) \]
In this reaction, the reactants are carbon monoxide (CO) and oxygen (\( \frac{1}{2} O_2 \)), and the product is carbon dioxide (CO2).

### Step 2: Determine the Change in Moles of Gas (\( \Delta N_g \))
To find \( \Delta N_g \), we need to calculate the number of moles of gaseous products and subtract the number of moles of gaseous reactants.

- Moles of gaseous products = 1 (from CO2)
- Moles of gaseous reactants = 1 (from CO) + \( \frac{1}{2} \) (from \( \frac{1}{2} O_2 \)) = \( 1 + 0.5 = 1.5 \)

Now, calculate \( \Delta N_g \):
\[ \Delta N_g = \text{Moles of products} - \text{Moles of reactants} = 1 - 1.5 = -0.5 \]

### Step 3: Use the Relationship Between \( K_p \) and \( K_c \)
The relationship between \( K_p \) and \( K_c \) is given by the equation:
\[ K_p = K_c \cdot (RT)^{\Delta N_g} \]
where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin.

### Step 4: Substitute \( \Delta N_g \) into the Equation
Substituting \( \Delta N_g = -0.5 \) into the equation:
\[ K_p = K_c \cdot (RT)^{-0.5} \]

### Step 5: Rearranging to Find \( \frac{K_p}{K_c} \)
We can rearrange the equation to find the ratio \( \frac{K_p}{K_c} \):
\[ \frac{K_p}{K_c} = (RT)^{-0.5} \]
This can also be expressed as:
\[ \frac{K_p}{K_c} = \frac{1}{\sqrt{RT}} \]

### Final Result
Thus, the ratio \( \frac{K_p}{K_c} \) for the given reaction is:
\[ \frac{K_p}{K_c} = \frac{1}{\sqrt{RT}} \]