Find out the units of `K_c and K_p` for the following equilibrium reactions :
` PCl_5(g) hArr PCl_3 + Cl_2(g)`

Answer

To find the units of \( K_c \) and \( K_p \) for the equilibrium reaction:

\[ PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g) \]

we will follow these steps:

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

The equilibrium constant \( K_c \) is defined in terms of the concentrations of the products and reactants. For the given reaction, the expression for \( K_c \) is:

\[ K_c = \frac{[PCl_3][Cl_2]}{[PCl_5]} \]

### Step 2: Determine the change in moles of gas (\( \Delta n \))

To find \( \Delta n \), we use the formula:

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

In this reaction:
- Products: \( PCl_3 + Cl_2 \) → 2 moles of gas
- Reactants: \( PCl_5 \) → 1 mole of gas

Thus,

\[ \Delta n = 2 - 1 = 1 \]

### Step 3: Find the units of \( K_c \)

The units of \( K_c \) can be derived from its expression. Since \( K_c \) is based on concentrations (moles per liter), the units become:

\[ \text{Units of } K_c = \left( \frac{\text{moles}}{\text{liters}} \right)^{\Delta n} = \left( \frac{\text{moles}}{\text{liters}} \right)^{1} = \frac{\text{moles}}{\text{liters}} = \text{mol/L} \]

### Step 4: Find the units of \( K_p \)

The equilibrium constant \( K_p \) is defined in terms of the partial pressures of the products and reactants. The expression for \( K_p \) is:

\[ K_p = \frac{P_{PCl_3} \cdot P_{Cl_2}}{P_{PCl_5}} \]

The units of pressure are typically in atmospheres (atm), so the units of \( K_p \) become:

\[ \text{Units of } K_p = \left( \text{atm} \right)^{\Delta n} = \left( \text{atm} \right)^{1} = \text{atm} \]

### Final Answer

- The units of \( K_c \) are \( \text{mol/L} \).
- The units of \( K_p \) are \( \text{atm} \).

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