At 500^oC,cyclopropane (C₃H₆)reacts to form its isomer,propene (C₃H₆).The reaction is first-order,and the rate constant is 6.7 × 10^-4 s^-1.If the initial concentration of cyclopropane is 0.500 M and the initial concentration of propene is 0,determine the time required for the concentration of propene to reach 0.100 M.

Question

Quizplus · Accepted Answer

The reaction is first-order, so we can use the integrated rate law: ln([C₃H₆]/[C₃H₆]0) = -kt where [C₃H₆] is the concentration of cyclopropane at any given time, [C₃H₆]0 is the initial concentration of cyclopropane, k is the rate constant, and t is the time. To find the time required for the concentration of propene to reach 0.100 M, we can use the fact that the initial concentration of propene is 0 and the balanced chemical equation for the reaction: C₃H₆ → C₃H₆ The stoichiometry of the reaction tells us that for every 1 mol of cyclopropane that reacts, 1 mol of propene is produced. Therefore, when the concentration of propene reaches 0.100 M, the concentration of cyclopropane will have decreased by 0.100 M as well. So we can plug in the given values and solve for t: ln([0.500 - 0.100]/0.500) = -6.7 × 10^-4 t t = ln(0.8/0.5) / (6.7 × 10^-4) = 3.3 × 10^12 s which is approximately equal to 3.3 × 10^10 seconds or 1042 years. Therefore, the best choice is B.

At 500oC,cyclopropane (C3H6)reacts to Form Its Isomer,propene (C3H6)

At 500^oC,cyclopropane (C₃H₆)reacts to Form Its Isomer,propene (C₃H₆)