The rate constant for this second‑order reaction is 0.950 M−1⋅s−1 at 300 ∘C. A⟶products

Question

How long, in seconds, would it take for the concentration of A to decrease from 0.740 M to 0.270 M?

Answer 1

second-order rate equation = k * [A]^2

reads as rate constant (k) times the concentration raises to the second power

rate = k * [A] * [A]

the time dependence of the concentration is given by

where [A] is the concentration at time t and [A]₀ is the initial concentration at zero time (the start)

the given information is rate constant ..... k = 0.950 M^-1s^-1 = 0.950 / Ms

given [A]₀ = 0.740 M, take the reciprocal using a calculator and write it down

given[A] = 0.270 M, take the reciprocal using a calculator and write it down

1 / [A]₀ = __________

1 / [A] = __________

notice that the unit M is in the denominator and you can group them on the left

as 1 / [A] minus 1 / [A]₀

divide by the rate constant and you've solved for time it takes in seconds for observed reaction to occur