For a reaction , the reactant concentration decreases 20% in 1 hr and 40% in 2hr. What are the units of rate constant ?

Answer

To determine the units of the rate constant for the given reaction, we need to analyze the information provided and understand the order of the reaction.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- We know that the concentration of the reactant decreases by 20% in 1 hour and by 40% in 2 hours. This indicates that the rate of reaction is constant over time, suggesting a zero-order reaction.

2. **Defining Zero-Order Reaction**:
- In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant. The rate can be expressed as:
\[ \text{Rate} = k[A]^0 = k \]
- Here, \( k \) is the rate constant and \([A]\) is the concentration of the reactant.

3. **Rate of Reaction**:
- The rate of a zero-order reaction can also be defined as the change in concentration over time:
\[ \text{Rate} = -\frac{d[A]}{dt} \]
- Since the concentration decreases by 20% in 1 hour, we can express this mathematically. If we assume the initial concentration of the reactant \([A]_0\) is 100 units, then:
- After 1 hour: \([A] = 80\) units (20% decrease)
- After 2 hours: \([A] = 60\) units (40% decrease)

4. **Calculating the Rate**:
- The average rate over the first hour is:
\[ \text{Rate} = \frac{\Delta [A]}{\Delta t} = \frac{80 - 100}{1 \text{ hr}} = -20 \text{ units/hr} \]
- The average rate over the second hour is:
\[ \text{Rate} = \frac{60 - 80}{1 \text{ hr}} = -20 \text{ units/hr} \]
- This confirms that the rate is constant at -20 units/hr.

5. **Units of the Rate Constant (k)**:
- For a zero-order reaction, the units of the rate constant \( k \) can be derived from the rate equation:
\[ \text{Rate} = k \]
- Since the rate is measured in concentration per time, the units of \( k \) are:
\[ k = \text{concentration/time} = \text{mol/L/s} \text{ or } \text{mol/L/hr} \]
- In this case, since we are dealing with hours, the units of the rate constant \( k \) for this zero-order reaction are:
\[ k = \text{mol/L/hr} \]

### Final Answer:
The units of the rate constant \( k \) for the reaction are **mol/L/hr**.