A first order reaction is `20%` complete in 10 minutes. Calculate the time taken for the reaction to go to `80%` completion.

Explanation

To solve the problem step by step, we will use the first-order kinetics equation and the information given in the question.

### Step 1: Understand the Reaction Completion
Given that the reaction is 20% complete in 10 minutes, we can denote the initial concentration of the reactant as \( [A]_0 = A \). When the reaction is 20% complete, the concentration of the reactant that has reacted is:
\[ x = 0.20 \times A = \frac{A}{5} \]
Thus, the concentration of the unreacted reactant at this point is:
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