Unit of equilibrium constant `K_p` for the reaction `PCl_5(g) hArr PCl_3(g)+ Cl_2(g)` is

Options

A. `atm`
B. `atm^-1`
C. `atm^2`
D. `atm^-2`

Answer

To find the unit of the equilibrium constant \( K_p \) for the reaction

\[ \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g), \]

we need to follow these steps:

### Step 1: Write the expression for \( K_p \)

The equilibrium constant \( K_p \) is defined in terms of the partial pressures of the gases involved in the reaction. For the given reaction, the expression for \( K_p \) is:

\[ K_p = \frac{P_{\text{PCl}_3} \cdot P_{\text{Cl}_2}}{P_{\text{PCl}_5}} \]

where \( P_{\text{PCl}_3} \), \( P_{\text{Cl}_2} \), and \( P_{\text{PCl}_5} \) are the partial pressures of PCl3, Cl2, and PCl5, respectively.

### Step 2: Assign units to the partial pressures

The partial pressures of gases are typically measured in atmospheres (atm). Therefore, we can assign the following units:

- \( P_{\text{PCl}_3} \) has units of atm
- \( P_{\text{Cl}_2} \) has units of atm
- \( P_{\text{PCl}_5} \) has units of atm

### Step 3: Substitute the units into the \( K_p \) expression

Substituting the units into the expression for \( K_p \):

\[ K_p = \frac{(\text{atm}) \cdot (\text{atm})}{\text{atm}} = \frac{\text{atm}^2}{\text{atm}} = \text{atm} \]

### Step 4: Conclusion

Thus, the unit of the equilibrium constant \( K_p \) for the reaction is:

\[ \text{atm} \]

### Final Answer

The correct option is **1. Atmosphere**.

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