For the reaction `CO(g)+Cl_(2)(g)hArrCOCl_(2)(g)`the value of `(K_(c)/(K_(P)))` is equal to :

Options

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

Answer

To solve the problem of finding the value of \( \frac{K_c}{K_p} \) for the reaction

\[ CO(g) + Cl_2(g) \rightleftharpoons COCl_2(g) \]

we can follow these steps:

### Step 1: Understand the relationship between \( K_c \) and \( K_p \)

The relationship between the equilibrium constants \( K_c \) (concentration-based) and \( K_p \) (pressure-based) is given by the formula:

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

where:
- \( R \) is the universal gas constant (0.0821 L·atm/(K·mol)),
- \( T \) is the temperature in Kelvin,
- \( \Delta n \) is the change in the number of moles of gas.

### Step 2: Calculate \( \Delta n \)

To find \( \Delta n \), we need to determine the number of moles of gaseous products and reactants.

- **Products**: There is 1 mole of \( COCl_2 \).
- **Reactants**: There are 1 mole of \( CO \) and 1 mole of \( Cl_2 \), totaling 2 moles.

Now we can calculate \( \Delta n \):

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

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

Now we substitute \( \Delta n \) into the relationship between \( K_c \) and \( K_p \):

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

This can be rearranged to find \( \frac{K_c}{K_p} \):

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

### Step 4: Conclusion

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

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

### Final Answer

The correct answer is \( RT \).

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