Phosgene, `COCl_(2)`, a poisonous gas decomposes according to the equation
`COCl_(2)(g)hArrCO(g)+Cl_(2)(g)`
If `K_(c)=0.083` at `900^(@)C`, What is the value of `K_(p)`?

Options

A. 0.125
B. `8.0`
C. `6.1`
D. `0.16`

Answer

To find the value of \( K_p \) from the given \( K_c \), we can use the relationship between \( K_p \) and \( K_c \):

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

### Step 1: Identify the reaction and calculate \( \Delta n \)
The given decomposition reaction is:

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

In this reaction:
- The number of moles of gaseous reactants (on the left) = 1 (from \( COCl_2 \))
- The number of moles of gaseous products (on the right) = 1 (from \( CO \)) + 1 (from \( Cl_2 \)) = 2

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

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

### Step 2: Convert temperature to Kelvin
The given temperature is \( 900^\circ C \). We need to convert this to Kelvin:

\[ T(K) = 900 + 273 = 1173 \, K \]

### Step 3: Use the ideal gas constant \( R \)
The ideal gas constant \( R \) is typically used in L·atm/(K·mol), but we will use it in the appropriate units for our calculations.

\[ R = 0.0821 \, L \cdot atm/(K \cdot mol) \]

### Step 4: Substitute values into the equation for \( K_p \)
Now we can substitute the values into the equation:

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

Substituting the known values:

\[ K_p = 0.083 \times (0.0821 \times 1173)^{1} \]

Calculating \( RT \):

\[ RT = 0.0821 \times 1173 \approx 96.4 \]

Now substituting this back into the equation for \( K_p \):

\[ K_p = 0.083 \times 96.4 \approx 8.00 \]

### Final Calculation
Thus, the value of \( K_p \) is approximately:

\[ K_p \approx 8.00 \]

### Summary of Steps
1. Identify the reaction and calculate \( \Delta n \).
2. Convert the temperature from Celsius to Kelvin.
3. Use the ideal gas constant \( R \).
4. Substitute the values into the equation for \( K_p \) and calculate.