If a reaction involves gaseous reactants and Products, the units of its rate are

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understand the Definition of Rate**:
The rate of a reaction is defined as the change in concentration of a reactant or product over time. Mathematically, this can be expressed as:
\[ \text{Rate} = -\frac{d[A]}{dt} \]
where \([A]\) is the concentration of the reactant A, and \(t\) is time.

2. **Identify the Units of Concentration**:
The concentration of a substance is typically expressed in moles per liter (mol/L), which can also be written as:
\[ \text{Concentration} = \text{mol} \cdot \text{L}^{-1} \]

3. **Incorporate Time into the Rate Expression**:
Since the rate is the change in concentration over time, we need to include the unit of time. If we consider time in seconds, the unit for the rate becomes:
\[ \text{Rate} = -\frac{d[A]}{dt} \Rightarrow \text{Units of Rate} = \frac{\text{mol} \cdot \text{L}^{-1}}{\text{s}} = \text{mol} \cdot \text{L}^{-1} \cdot \text{s}^{-1} \]

4. **Relate Concentration to Pressure**:
For gaseous reactants and products, we can relate concentration to pressure using the ideal gas law:
\[ PV = nRT \Rightarrow P = \frac{n}{V}RT \]
Here, \(P\) (pressure) can be expressed in terms of concentration since \(C = \frac{n}{V}\). Thus, at constant temperature, pressure is directly proportional to concentration.

5. **Express Rate in Terms of Pressure**:
Therefore, we can express the rate in terms of pressure:
\[ \text{Rate} = -\frac{dP}{dt} \]

6. **Determine the Units of Pressure**:
If we consider the unit of pressure as atmospheres (atm), then the unit of the rate becomes:
\[ \text{Units of Rate} = \frac{\text{atm}}{\text{s}} = \text{atm} \cdot \text{s}^{-1} \]

### Final Answer:
The units of the rate for a reaction involving gaseous reactants and products are:
\[ \text{atm} \cdot \text{s}^{-1} \]