For the reaction, `CO_((g))+Cl_(2(g))hArrCoCl_(2(g))`, the value of `K_(p)//K_(c)` is equal to

Options

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

Answer

To find the value of \( \frac{K_p}{K_c} \) for the reaction

\[ CO_{(g)} + Cl_{2(g)} \rightleftharpoons COCl_{2(g)}, \]

we will follow these steps:

### Step 1: Identify the reaction and the components
The reaction involves the gaseous reactants carbon monoxide (CO) and chlorine (Cl2) forming the gaseous product carbonyl chloride (COCl2).

### Step 2: Write the expression for \( K_p \) and \( K_c \)
The equilibrium constants are defined as follows:
- \( K_c \) is based on the concentrations of the reactants and products.
- \( K_p \) is based on the partial pressures of the reactants and products.

### Step 3: Use the relationship between \( K_p \) and \( K_c \)
The relationship between \( K_p \) and \( K_c \) is given by the equation:

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

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

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

### Step 4: Calculate \( \Delta n \)
In our reaction:
- Products: 1 mole of \( COCl_2 \)
- Reactants: 1 mole of \( CO \) + 1 mole of \( Cl_2 \) = 2 moles

Thus,

\[ \Delta n = 1 - 2 = -1 \]

### Step 5: Substitute \( \Delta n \) into the equation
Now substituting \( \Delta n \) into the relationship:

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

### Step 6: Rearrange to find \( \frac{K_p}{K_c} \)
To find \( \frac{K_p}{K_c} \):

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

### Final Answer
Thus, the value of \( \frac{K_p}{K_c} \) is:

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