Unit of equilibrium constant is:

Options

A. `(mol L^(-1))^(1-n)`
B. `(mol L^(-1))^(Deltan)`
C. `(atm)^(Deltan)`
D. All

Answer

To determine the unit of the equilibrium constant, we need to understand the definitions of \( K_c \) and \( K_p \) and how to calculate them based on the stoichiometry of a given chemical reaction.

### Step-by-Step Solution:

1. **Understand the Equilibrium Constant**:
- The equilibrium constant \( K_c \) is used for reactions in terms of concentration (molarity), while \( K_p \) is used for reactions in terms of partial pressures.

2. **Define \( K_c \)**:
- For a general reaction:
\[ aA + bB \rightleftharpoons cC + dD \]
- The expression for \( K_c \) is given by:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]
- Here, \([A]\), \([B]\), \([C]\), and \([D]\) are the molar concentrations of the reactants and products.

3. **Calculate the Change in Moles (\( \Delta n \))**:
- \( \Delta n \) is defined as:
\[ \Delta n = (c + d) - (a + b) \]
- This represents the change in the number of moles of gaseous products minus the number of moles of gaseous reactants.

4. **Determine the Units of \( K_c \)**:
- The units of \( K_c \) can be derived from the expression:
\[ K_c = \frac{[\text{products}]}{[\text{reactants}]} \]
- The units of concentration are moles per liter (mol/L). Therefore, the units of \( K_c \) can be expressed as:
\[ K_c \text{ units} = \left( \text{mol/L} \right)^{\Delta n} = \text{mol}^{\Delta n} \cdot \text{L}^{-\Delta n} \]
- This can also be written as:
\[ \text{mol} \cdot \text{L}^{-1} \text{ whole}^{\Delta n} \]

5. **Define \( K_p \)**:
- For the same reaction, the expression for \( K_p \) is given by:
\[ K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b} \]
- Here, \( P \) represents the partial pressures of the gases involved in the reaction.

6. **Determine the Units of \( K_p \)**:
- The units of pressure are typically in atmospheres (atm). Therefore, the units of \( K_p \) can be expressed as:
\[ K_p \text{ units} = \text{atm}^{\Delta n} \]

### Summary of Units:
- The unit of \( K_c \) is \( \text{mol}^{\Delta n} \cdot \text{L}^{-\Delta n} \) or \( \text{mol} \cdot \text{L}^{-1} \text{ whole}^{\Delta n} \).
- The unit of \( K_p \) is \( \text{atm}^{\Delta n} \).