For the reactions,
` CO(g) +Cl_2( g) hArr COCl_2(g), " the " (K_P)/(K_c) ` is equal to

Options

A. ` (1)/( RT) `
B. RT
C. ` sqrt(RT) `
D. ` 1.0 `

Explanation

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

\[ \text{CO(g)} + \text{Cl}_2(g) \rightleftharpoons \text{COCl}_2(g) \]

we can follow these steps:

### Step 1: Write the expression for \( K_p \) and \( K_c \)

For the reaction, the equilibrium constant in terms of partial pressures (\( K_p \)) and concentrations (\( K_c \)) can be defined as follows:

- \( K_p = \frac{P_{\text{COCl}_2}}{P_{\text{CO}} \cdot P_{\text{Cl}_2}} \)
- \( K_c = \frac{[COCl_2]}{[CO] \cdot [Cl_2]} \)

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

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

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

where:
- \( R \) is the universal gas constant,
- \( T \) is the temperature in Kelvin,
- \( \Delta N_g \) is the change in the number of moles of gas.

### Step 3: Calculate \( \Delta N_g \)

To find \( \Delta N_g \), we need to determine the change in the number of moles of gaseous products and reactants:

- Moles of gaseous products: 1 (from \( \text{COCl}_2 \))
- Moles of gaseous reactants: 2 (1 from \( \text{CO} \) and 1 from \( \text{Cl}_2 \))

Thus,

\[ \Delta N_g = \text{(moles of products)} - \text{(moles of reactants)} = 1 - 2 = -1 \]

### Step 4: Substitute \( \Delta N_g \) into the equation

Now, substituting \( \Delta N_g \) into the relationship:

\[ K_p = K_c \cdot (RT)^{-1} \]

### Step 5: Rearranging for \( \frac{K_p}{K_c} \)

To find \( \frac{K_p}{K_c} \):

\[ \frac{K_p}{K_c} = \frac{K_c \cdot (RT)^{-1}}{K_c} = \frac{1}{RT} \]

### Final Answer

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

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