If the first order reaction involves gaseous reactant & gaseous products, the units of its rate are

Options

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

Answer

To determine the units of the rate for a first-order reaction involving gaseous reactants and products, we can follow these steps:

### Step 1: Understand the Rate Law for a First-Order Reaction
For a first-order reaction, the rate can be expressed as:
\[ \text{Rate} = k[A] \]
where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant.

### Step 2: Identify the Units of Concentration
In this case, since the reactants and products are gases, we can express the concentration in terms of partial pressure. The unit of concentration can be expressed in terms of pressure, typically in atmospheres (ATM).

### Step 3: Determine the Units of the Rate Constant
For a first-order reaction, the units of the rate constant \( k \) are:
\[ \text{Units of } k = \text{time}^{-1} \]
If we take time in seconds, then:
\[ \text{Units of } k = \text{s}^{-1} \]

### Step 4: Combine the Units to Find the Rate
The rate of the reaction, which is expressed in terms of concentration (or partial pressure), will have the units:
\[ \text{Rate} = k[A] \]
Substituting the units:
\[ \text{Rate} = (\text{s}^{-1})(\text{ATM}) \]
Thus, the units of the rate will be:
\[ \text{Rate} = \text{ATM} \cdot \text{s}^{-1} \]

### Conclusion
Therefore, the units of the rate for a first-order reaction involving gaseous reactants and products are:
\[ \text{ATM} \cdot \text{s}^{-1} \]