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

Options

A. `PCl_(5)(g) hArr PCl_(3)(g)+Cl_(2)(g)`
B. `AB_(2)(g) hArr AB(g)+B(g)`
C. `NH_(4)HS(s) hArr NH_(3)(g)+H_(2)S(g)`
D. `2NH_(3)(g) hArr N_(2)(g)+3H_(2)(g)`

Explanation

To solve the problem of determining which reactions have the same units of \( K_p \), we will analyze each reaction step by step.

### Step 1: Understand the relationship between \( K_p \) and partial pressures
The equilibrium constant \( K_p \) is defined in terms of the partial pressures of the gaseous reactants and products. The general formula for \( K_p \) is:

\[ K_p = \frac{(P_{\text{products}})^{\text{stoichiometric coefficients}}}{(P_{\text{reactants}})^{\text{stoichiometric coefficients}}} \]

### Step 2: Analyze each reaction

**Reaction 1:**
\[ \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \]
For this reaction:
\[ K_p = \frac{(P_{\text{PCl}_3})^1 \cdot (P_{\text{Cl}_2})^1}{(P_{\text{PCl}_5})^1} \]
Units:
\[ K_p = \frac{(\text{atm})^1 \cdot (\text{atm})^1}{(\text{atm})^1} = \text{atm} \]

**Reaction 2:**
\[ \text{AB}_2(g) \rightleftharpoons \text{AB}(g) + \text{B}(g) \]
For this reaction:
\[ K_p = \frac{(P_{\text{AB}})^1 \cdot (P_{\text{B}})^1}{(P_{\text{AB}_2})^1} \]
Units:
\[ K_p = \frac{(\text{atm})^1 \cdot (\text{atm})^1}{(\text{atm})^1} = \text{atm} \]

**Reaction 3:**
\[ \text{NH}_4\text{HS}(s) \rightleftharpoons \text{NH}_3(g) + \text{H}_2\text{S}(g) \]
For this reaction:
\[ K_p = \frac{(P_{\text{NH}_3})^1 \cdot (P_{\text{H}_2\text{S}})^1}{(P_{\text{NH}_4\text{HS}})^1} \]
Since \( \text{NH}_4\text{HS} \) is a solid, it does not appear in the expression:
\[ K_p = (P_{\text{NH}_3})^1 \cdot (P_{\text{H}_2\text{S}})^1 \]
Units:
\[ K_p = (\text{atm})^1 \cdot (\text{atm})^1 = \text{atm}^2 \]

**Reaction 4:**
\[ 2\text{NH}_3(g) \rightleftharpoons \text{N}_2(g) + 3\text{H}_2(g) \]
For this reaction:
\[ K_p = \frac{(P_{\text{N}_2})^1 \cdot (P_{\text{H}_2})^3}{(P_{\text{NH}_3})^2} \]
Units:
\[ K_p = \frac{(\text{atm})^1 \cdot (\text{atm})^3}{(\text{atm})^2} = \frac{\text{atm}^4}{\text{atm}^2} = \text{atm}^2 \]

### Step 3: Compare the units of \( K_p \)
- **Reactions 1 and 2:** Both have units of \( \text{atm} \).
- **Reactions 3 and 4:** Both have units of \( \text{atm}^2 \).

### Conclusion
The reactions that have the same units of \( K_p \) are:
- **Reactions 1 and 2** (units of \( K_p \) = atm)
- **Reactions 3 and 4** (units of \( K_p \) = atm²)