Final answer:
The half-life of a first-order reaction can be calculated by determining the rate constant 'k' from the percent completion and the time taken. Then, using the equation t₁/2 = 0.693/k, the half-life is found.
Step-by-step explanation:
To calculate the half-life for a certain first-order reaction that is 71 percent complete in 65 seconds, we use the fact that the half-life of a first-order reaction is constant and independent of concentration. A first-order reaction is 50% complete after one half-life, so the key is to determine the time it takes for the reaction to reach that level of completion. We use the first-order decay equation:
ln([A]/[A]₀) = -kt
Since the reaction is 71% complete, 29% of the original concentration of the reactant remains. Substituting this into the decay equation gives us:
ln(0.29) = -k * 65 s
From the equation, we can solve for the rate constant k and then use the first-order half-life equation t₁/2 = 0.693/k to find the half-life.