Rate constant determination in a reaction
Determining the unit of rate constant in a reaction involves looking at the rate of decomposition of the reactant over time. Let's break down the information provided in the question and analyze how we can determine the unit of the rate constant.

Given information:
- 20% of reactant decomposes in 1 hour
- 40% decomposes in 2 hours
- 60% decomposes in 3 hours
- and so on

Analysis:
- In the first hour, 20% of the reactant decomposes, meaning the reaction rate is 20% per hour.
- In the second hour, an additional 20% decomposes, so the total rate of decomposition is 40% per 2 hours.
- This pattern continues, with each subsequent hour adding an additional 20% to the total rate of decomposition.

Determination of rate constant:
- The rate constant (k) is a proportionality constant that relates the rate of reaction to the concentration of reactants.
- In this case, since the rate of decomposition is increasing by 20% each hour, the unit of the rate constant would be per hour.
- Therefore, the unit of the rate constant in this reaction would be per hour (h^-1).

Conclusion:
- By analyzing the rate of decomposition of the reactant over time, we can determine that the unit of the rate constant in this reaction is per hour (h^-1). This information is crucial for understanding the kinetics of the reaction and predicting its behavior under different conditions.