Given:
- First order reaction
- 40% complete in 20 minutes

To find:
- Time required for the reaction to be 50% complete

Explanation:

1. Understanding First Order Reaction:
- In a first order reaction, the rate of reaction is directly proportional to the concentration of the reactant.
- The mathematical expression for a first order reaction is: Rate = k[A], where [A] is the concentration of reactant A and k is the rate constant.

2. Integrated Rate Law:
- The integrated rate law for a first order reaction is given by the equation: ln([A]t/[A]0) = -kt, where [A]t is the concentration of reactant A at time t, [A]0 is the initial concentration of reactant A, k is the rate constant, and t is the time.

3. Determining the Rate Constant:
- We can use the information given to determine the rate constant (k) for the reaction.
- Since the reaction is 40% complete in 20 minutes, we can write the following equation: ln(0.4) = -k * 20.
- Solving this equation for k, we find k = ln(0.4) / -20.

4. Finding the Time for 50% Completion:
- We need to find the time required for the reaction to be 50% complete.
- Using the integrated rate law equation, we can write: ln(0.5) = (-k) * t.
- Substituting the value of k obtained in the previous step, we have ln(0.5) = (ln(0.4) / -20) * t.
- Solving this equation for t, we find t = (-20 * ln(0.5)) / ln(0.4).

Answer:
The time required for the reaction to be 50% complete is (-20 * ln(0.5)) / ln(0.4) minutes.