A first order reaction has a half-life of 8.50 min. Starting from 0.150 mol/L, how long until the concentration falls to 0.0300 mol/L?

1. Recover the rate constant from the half-life: k = 0.693 / 8.50 min = 0.0815 per minute. 2. The concentration must fall by a factor of 0.150 / 0.0300 = 5. 3. Apply the integrated law: t = ln(5) / k. 4. With ln 5 = 1.609, the time is 1.609 / 0.0815 per minute = 19.7 min. 5. Units check: a pure number over per minute leaves minutes. 6. Sanity check: a factor of 5 sits between 2 half-lives (factor 4) and 3 half-lives (factor 8), and 19.7 min is between 17.0 and 25.5 min. 7. The value 42.5 min treats a fivefold drop as five half-lives. 8. The value 17.0 min assumes two half-lives, a factor of four rather than five, and 4.25 min halves the half-life for no reason. _Source: OpenStax Chemistry (CC BY 4.0), Ch 12 "Kinetics", section 12.4 Integrated Rate Laws_