The unit of first order rate constant when concentration is measured in terms of pressure and time in minutes is ………………. .

Answer

To determine the unit of the first-order rate constant (k) when concentration is measured in terms of pressure and time is measured in minutes, we can follow these steps:

### Step-by-Step Solution:

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

2. **Substituting Pressure for Concentration**:
In this case, we are measuring concentration in terms of pressure. Thus, we can rewrite the equation as:
\[ \text{Rate} = k \cdot P \]
where \( P \) is the pressure of the reactant.

3. **Understanding the Units**:
The unit of rate is typically expressed in terms of change in concentration over time. For a first-order reaction, the rate can also be expressed as:
\[ \text{Rate} = -\frac{dP}{dt} \]
where \( dP \) is the change in pressure and \( dt \) is the change in time.

4. **Setting Up the Units**:
The units for the rate (change in pressure over time) can be expressed as:
\[ \text{Units of Rate} = \frac{\text{Pressure}}{\text{Time}} = \frac{\text{Pressure}}{\text{Minutes}} \]

5. **Relating Units to Rate Constant**:
From the rate equation \( \text{Rate} = k \cdot P \), we can rearrange to find the units of \( k \):
\[ k = \frac{\text{Rate}}{P} \]
Substituting the units we have:
\[ \text{Units of } k = \frac{\frac{\text{Pressure}}{\text{Minutes}}}{\text{Pressure}} = \frac{1}{\text{Minutes}} = \text{Minute}^{-1} \]

6. **Final Answer**:
Therefore, the unit of the first-order rate constant when concentration is measured in terms of pressure and time is measured in minutes is:
\[ \text{Minute}^{-1} \]