`K_(p)` and `K_(c)` are inter related as
`K_(p)=K_(c)(RT)^(Deltan)`
Answer the following questions:
Which of the following have `K_(p)=K_(c)`?

Options

A. `H_(2)(g)+I_(2)(g) hArr 2HI(g)`
B. `N_(2)(g)+O_(2)(g) hArr 2NO(g)`
C. `2NO(g)+Cl_(2)(g) harr 2NOCl(g)`
D. `2SO_(2)(g)+O_(2)(g) harr 2SO_(3)(g)`

Explanation

To determine which of the given reactions have \( K_p = K_c \), we will use the relationship:

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

Where:
- \( \Delta n_g \) is the change in the number of moles of gas, calculated as the moles of gaseous products minus the moles of gaseous reactants.

### Step-by-Step Solution:

1. **Identify the reactions:**
- Reaction 1: \( H_2(g) + I_2(g) \rightarrow 2HI(g) \)
- Reaction 2: \( N_2(g) + O_2(g) \rightarrow 2NO(g) \)
- Reaction 3: \( 2NO(g) + Cl_2(g) \rightarrow 2NOCl(g) \)
- Reaction 4: \( 2SO_2(g) + O_2(g) \rightarrow 2SO_3(g) \)

2. **Calculate \( \Delta n_g \) for each reaction:**
- For Reaction 1:
- Moles of products = 2 (from \( 2HI \))
- Moles of reactants = 1 (from \( H_2 \)) + 1 (from \( I_2 \)) = 2
- \( \Delta n_g = 2 - 2 = 0 \)

- For Reaction 2:
- Moles of products = 2 (from \( 2NO \))
- Moles of reactants = 1 (from \( N_2 \)) + 1 (from \( O_2 \)) = 2
- \( \Delta n_g = 2 - 2 = 0 \)

- For Reaction 3:
- Moles of products = 2 (from \( 2NOCl \))
- Moles of reactants = 2 (from \( 2NO \)) + 1 (from \( Cl_2 \)) = 3
- \( \Delta n_g = 2 - 3 = -1 \)

- For Reaction 4:
- Moles of products = 2 (from \( 2SO_3 \))
- Moles of reactants = 2 (from \( 2SO_2 \)) + 1 (from \( O_2 \)) = 3
- \( \Delta n_g = 2 - 3 = -1 \)

3. **Determine when \( K_p = K_c \):**
- From the relationship \( K_p = K_c (RT)^{\Delta n_g} \), we find that \( K_p = K_c \) when \( \Delta n_g = 0 \).
- From our calculations, we see that \( \Delta n_g = 0 \) for Reaction 1 and Reaction 2.

4. **Conclusion:**
- Therefore, \( K_p = K_c \) for:
- Reaction 1: \( H_2(g) + I_2(g) \rightarrow 2HI(g) \)
- Reaction 2: \( N_2(g) + O_2(g) \rightarrow 2NO(g) \)

### Final Answer:
The reactions for which \( K_p = K_c \) are:
- Option 1: \( H_2 + I_2 \rightarrow 2HI \)
- Option 2: \( N_2 + O_2 \rightarrow 2NO \)

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