The unit of equilibrium constant, K for the reaction, `A+B rarr C` , would be

Options

A. `molL^(-1)`
B. molL
C. `Lmol^(-1)`
D. Dimensionless

Explanation

To find the unit of the equilibrium constant \( K \) for the reaction \( A + B \rightleftharpoons C \), we can follow these steps:

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

The equilibrium constant \( K_c \) for a reaction is given by the formula:

\[ K_c = \frac{[\text{products}]^{\text{stoichiometric coefficient}}}{[\text{reactants}]^{\text{stoichiometric coefficient}}} \]

For the reaction \( A + B \rightleftharpoons C \), the expression becomes:

\[ K_c = \frac{[C]^1}{[A]^1 [B]^1} \]

### Step 2: Identify the units of concentration

The concentration of a substance in a solution is typically expressed in molarity, which has the unit of moles per liter (mol/L). In terms of units, we can denote this as:

\[ \text{Concentration unit} = M = \text{mol/L} \]

### Step 3: Substitute the units into the equilibrium constant expression

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

\[ K_c = \frac{[\text{C}]}{[\text{A}][\text{B}]} = \frac{M}{M \cdot M} = \frac{M}{M^2} \]

### Step 4: Simplify the expression

When we simplify the expression:

\[ K_c = \frac{M}{M^2} = M^{-1} \]

### Step 5: Express the unit in terms of moles and liters

Since \( M \) is equal to \( \frac{\text{mol}}{\text{L}} \), we can express \( M^{-1} \) as:

\[ M^{-1} = \frac{1}{\text{mol/L}} = \frac{\text{L}}{\text{mol}} \]

Thus, the unit of the equilibrium constant \( K \) for the reaction \( A + B \rightleftharpoons C \) is:

\[ \text{Unit of } K_c = \text{L/mol} \]

### Final Answer

The unit of equilibrium constant \( K \) for the reaction \( A + B \rightleftharpoons C \) is \( \text{L/mol} \).

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