The unit of equilibrium constant `(K_(c))` in general is

Options

A. (mol/lit)
B. (lit/mol)
C. `"(mol/lit)"^(trianglen)`
D. `"(lit/mol)"^(trianglen)`

Explanation

To determine the unit of the equilibrium constant \( K_c \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant**:
The equilibrium constant \( K_c \) is defined for a general reaction of the form:
\[ aA + bB \rightleftharpoons cC + dD \]
where \( A, B, C, D \) are the chemical species and \( a, b, c, d \) are their respective stoichiometric coefficients.

2. **Writing the Expression for \( K_c \)**:
The expression for the equilibrium constant \( K_c \) in terms of the concentrations of the reactants and products is given by:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]
Here, \([X]\) denotes the concentration of species \( X \) in moles per liter (mol/L).

3. **Substituting the Units**:
Since the concentration is expressed in moles per liter (mol/L), we can substitute this into the expression for \( K_c \):
\[ K_c = \frac{(\text{mol/L})^c (\text{mol/L})^d}{(\text{mol/L})^a (\text{mol/L})^b} \]

4. **Simplifying the Expression**:
This can be simplified to:
\[ K_c = \frac{(\text{mol})^{c+d}}{(\text{mol})^{a+b} \cdot (\text{L})^{a+b}} \]
Thus, we can write:
\[ K_c = \frac{\text{mol}^{c+d}}{\text{mol}^{a+b} \cdot \text{L}^{a+b}} = \text{mol}^{(c+d)-(a+b)} \cdot \text{L}^{-(a+b)} \]

5. **Defining \( \Delta n \)**:
Let \( \Delta n = (c + d) - (a + b) \). Therefore, we can express \( K_c \) as:
\[ K_c = \text{mol}^{\Delta n} \cdot \text{L}^{-(a+b)} \]

6. **Final Unit of \( K_c \)**:
The final unit of \( K_c \) can be expressed as:
\[ K_c = \text{mol}^{\Delta n} \cdot \text{L}^{- (a + b)} \]
In general, if \( \Delta n \) is the difference in the number of moles of products and reactants, the unit of \( K_c \) can be summarized as:
\[ K_c \text{ has units of } \text{mol}^{\Delta n} \cdot \text{L}^{- (a + b)} \]