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

The concentration of cyclobutane after 875 seconds is approximately 0.000961 M

Step-by-step 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} \frac {[A_t]}{[A_0]} = \text {-k} \cdot t }`

Therefore, we get;

`k = \frac{\text{ ln} \frac {[A_t]}{[A_0]}} {-t }`

Which gives;

`k = \frac{\text{ ln} \frac {0.00119}{0.00150}} {-455} \approx 5.088 * 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 * 10^(-4) * 875}` = 0.000961

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