`K_p//K_c` for the reaction `CO+1/2O_2 Leftrightarrow CO_2` is

Options

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

Answer

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

\[ \text{CO} + \frac{1}{2} \text{O}_2 \leftrightarrow \text{CO}_2, \]

we will follow these steps:

### Step 1: Identify the Reaction and Calculate \(\Delta N_g\)

The given reaction is:

\[ \text{CO} + \frac{1}{2} \text{O}_2 \leftrightarrow \text{CO}_2. \]

In this reaction:
- The number of moles of gaseous reactants (\(N_{reactants}\)) = 1 (from CO) + 0.5 (from \( \frac{1}{2} O_2 \)) = 1.5 moles.
- The number of moles of gaseous products (\(N_{products}\)) = 1 (from CO2).

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

\[ \Delta N_g = N_{products} - N_{reactants} = 1 - 1.5 = -0.5. \]

### Step 2: Use the Relationship Between \( K_p \) and \( K_c \)

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

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

where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin.

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

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

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

This can be rewritten as:

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

### Conclusion

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

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