For a reaction,
`H_2(g)+I_2(g) iff 2HI(g)`
`K_c=[HI(g)]^2/[H_2(g)[I_2(g)]`
Point out the correct statement.

Options

A. The subscript 'c' indicates that `K_c` is expressed in concentrations of `(mol)^_(-1) L`
B. The subscript 'c' indicates that `K_c` is expressed in concentrations of `mol L^(-1)`
C. The subscript 'c' indicates that `K_c` is expressed in active mass of `(mol)^_(-1) L`
D. The subscript 'c' indicates that `K_c` is expressed in active mass of `(mol) L^(-1)`

Answer

To solve the question regarding the reaction \( H_2(g) + I_2(g) \iff 2HI(g) \) and the equilibrium constant \( K_c \), we will analyze the given information step by step.

### Step 1: Understanding the Reaction
The reaction given is:
\[ H_2(g) + I_2(g) \iff 2HI(g) \]
This indicates that hydrogen gas (\( H_2 \)) and iodine gas (\( I_2 \)) react to form hydrogen iodide (\( HI \)).

### Step 2: Writing the Expression for \( K_c \)
The equilibrium constant \( K_c \) for this reaction is defined as:
\[ K_c = \frac{[HI]^2}{[H_2][I_2]} \]
where \([HI]\), \([H_2]\), and \([I_2]\) represent the molar concentrations of the respective gases at equilibrium.

### Step 3: Understanding the Subscript 'C'
The subscript 'C' in \( K_c \) indicates that the concentrations are expressed in terms of molarity (moles per liter). This is important for understanding the units of \( K_c \).

### Step 4: Determining the Units of \( K_c \)
The unit of molarity is:
\[ \text{Molarity} = \frac{\text{moles}}{\text{volume in liters}} = \text{mol/L} \]
Thus, the units for \( K_c \) can be derived from the expression:
- The numerator \([HI]^2\) has units of \((\text{mol/L})^2 = \text{mol}^2/\text{L}^2\).
- The denominator \([H_2][I_2]\) has units of \((\text{mol/L})(\text{mol/L}) = \text{mol}^2/\text{L}^2\).

Therefore, the units of \( K_c \) become:
\[ K_c = \frac{\text{mol}^2/\text{L}^2}{\text{mol}^2/\text{L}^2} = 1 \]
This means that \( K_c \) is dimensionless.

### Step 5: Analyzing the Statements
Now, we need to evaluate the statements provided in the question:
1. The subscript C indicates that \( K_c \) is expressed in concentration of mole inverse bracket inverse liter. (Incorrect)
2. The subscript C indicates that \( K_c \) is expressed in terms of concentration of mole per liter. (Correct)
3. The subscript C indicates that \( K_c \) is expressed in active mass of mole inverse liter. (Incorrect)
4. The subscript C indicates that \( K_c \) is expressed in active mass of mole per liter inverse. (Incorrect)

### Conclusion
The correct statement is:
**Option 2: The subscript C indicates that \( K_c \) is expressed in terms of concentration of mole per liter.**