Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ‘k’ value of 3.3 × — Chemical Kinetics Chemistry Question
Question
Gaseous cyclobutene isomerizes to butadiene in a first order process which has a ‘k’ value of 3.3 × 10 s at 153 C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is _______. (Rounded off to the nearest integer) -4 -1 o
💡 Solution & Explanation
**Step 1: Identify the first-order rate law equation** For a first-order reaction: $$\ln\left(\frac{[A]_0}{[A]_t}\right) = kt$$ **Step 2: Determine initial and remaining concentrations** If the reaction proceeds 40% to completion: - [A]₀ = 100 (initial, arbitrary units) - [A]ₜ = 60 (60% remains after 40% reacts) - Ratio: [A]₀/[A]ₜ = 100/60 = 1.667 **Step 3: Calculate the natural logarithm** $$\ln(1.667) = 0.511$$ **Step 4: Solve for time using the rate constant** Given: k = 3.3 × 10⁻⁴ s⁻¹ $$0.511 = (3.3 \times 10^{-4}) \times t$$ $$t = \frac{0.511}{3.3 \times 10^{-4}} = 1545.5 \text{ seconds}$$ **Step 5: Convert seconds to minutes** $$t = \frac{1545.5}{60} = 25.76 \text{ minutes}$$ **Step 6: Round to nearest integer** 25.76 ≈ 26 minutes Therefore, the answer is 26.00.