The rate constant for this second‑order reaction is 0.670 M - 1 ⋅ s - 1 at 300 ∘ C. A ⟶ products How long, in seconds, would it take for the concentration of A to decrease from 0.690 M to 0.360 M?

t = 1.983 s

Explanation:

A → Pdts - rA = K (CA) ∧α = - δCA/δt

∴ α: order = 2

∴ K: rate constant = 0.670/M. s ... T = 300°C

⇒ - δCA/δt = (0.670/M. s) (CA²)

⇒ - ∫δCA/CA² = (0.670) ∫δt

⇒ [ 1/CA - 1/CAo ] = 0.670*t

∴ CA = 0.360 M

∴ CAo = 0.690 M

⇒ [ 1/0.360 - 1/0.690 ] = 0.670*t

⇒ [ 1.3285/M ] = (0.670/M. s) * t

⇒ t = 1.983 s