Final answer:
To determine the half-life of a first-order reaction, use the formula t1/2 = (0.693/k) * log(initial concentration / remaining concentration), where k is the rate constant. Substituting the given values, we can solve for t1/2.
Step-by-step explanation:
In a first-order reaction, the concentration of a compound decreases by half in each successive half-life.
Given that 36.0% of the compound has decomposed after 52.0 min, we can use the formula:
t1/2 = (0.693/k)
Where t1/2 is the half-life and k is the rate constant. Since 36.0% of the compound has decomposed, then 1 - 0.36 = 0.64 remains. Hence, the reaction is 64% complete. Substituting the values into the formula:
t1/2 = (0.693/k) * log(initial concentration / remaining concentration)
t1/2 = (0.693/k) * log(1 / 0.64)
By solving for t1/2, we can determine the half-life of the reaction assuming first-order kinetics.
t1/2 = ????