For an equilibrium reaction involving gases, the forward reaction is first order while the reverse reaction is second order. The unit of `K_(p)` for forward equilibrium is

Options

A. atm
B. `atm^(2)`
C. `atm^(-1)`
D. `atm^(-2)`

Answer

To find the unit of \( K_p \) for the forward equilibrium reaction, we need to analyze the given information step by step.

### Step 1: Understand the Reaction Orders
The problem states that the forward reaction is first order and the reverse reaction is second order. This means:
- For the forward reaction, the rate can be expressed as:
\[ \text{Rate}_{\text{forward}} = k_f [A]^1 \]
where \( k_f \) is the rate constant for the forward reaction and \( [A] \) is the concentration of reactant A.

- For the reverse reaction, the rate can be expressed as:
\[ \text{Rate}_{\text{reverse}} = k_b [B]^2 \]
where \( k_b \) is the rate constant for the reverse reaction and \( [B] \) is the concentration of product B.

### Step 2: Write the Units of Rate Constants
The unit of the rate constant \( k \) depends on the order of the reaction:
- For a first-order reaction (forward):
\[ \text{Unit of } k_f = \text{M}^{1 - 1} \cdot \text{s}^{-1} = \text{s}^{-1} \]
(where M is mol/L or concentration).

- For a second-order reaction (reverse):
\[ \text{Unit of } k_b = \text{M}^{1 - 2} \cdot \text{s}^{-1} = \text{M}^{-1} \cdot \text{s}^{-1} \]

### Step 3: Convert Concentration Units to Pressure Units
Since we need to express \( K_p \) in terms of pressure, we convert the concentration units (M) to pressure units (atm). The conversion is based on the ideal gas law, where 1 M is approximately equal to 0.0821 atm at standard temperature and pressure.

- Thus, the unit of \( k_f \) in terms of pressure:
\[ k_f = \text{s}^{-1} \quad \text{(remains the same)} \]

- The unit of \( k_b \) in terms of pressure:
\[ k_b = \text{atm}^{-1} \cdot \text{s}^{-1} \]

### Step 4: Calculate the Unit of \( K_p \)
The equilibrium constant \( K_p \) is defined as:
\[ K_p = \frac{k_f}{k_b} \]
Substituting the units we found:
\[ \text{Unit of } K_p = \frac{\text{s}^{-1}}{\text{atm}^{-1} \cdot \text{s}^{-1}} = \text{atm} \]

### Conclusion
The unit of \( K_p \) for the forward equilibrium reaction is:
\[ \text{Unit of } K_p = \text{atm} \]