Question

Cyclobutane, C4H8, consisting of molecules in which four carbon atoms form a ring, decomposes, when heated, to give ethylene. The reaction is first order. In an experiment, the initial concentration of cyclobutane was 0.00150 M. After heating at 450°C for 455 s, this was reduced to 0.00119 M. What was the concentration of cyclobutane after a total of 875 s?

Answer 1

Answer:

The concentration of cyclobutane after 875 seconds is approximately 0.000961 M

Explanation:

The initial concentration of cyclobutane, C₄H₈, [A₀] = 0.00150 M

The final concentration of cyclobutane, [$A_t$] = 0.00119 M

The time for the reaction, t = 455 seconds

Therefore, the Rate Law for the first order reaction is presented as follows;

$\text{ ln} \dfrac {[A_t]}{[A_0]} = \text {-k} \cdot t }$

Therefore, we get;

$k = \dfrac{\text{ ln} \dfrac {[A_t]}{[A_0]}} {-t }$

Which gives;

$k = \dfrac{\text{ ln} \dfrac {0.00119}{0.00150}} {-455} \approx 5.088 \times 10^{-4}$

k ≈ 5.088 × 10⁻⁴ s⁻¹

The concentration after 875 seconds is given as follows;

[$A_t$] = [A₀]·$e^{-k \cdot t}$

Therefore;

[$A_t$] = 0.00150 × $e^{5.088 \times 10^{-4} \times 875}$  = 0.000961

The concentration of cyclobutane after 875 seconds, [$A_t$] ≈ 0.000961 M