# Problem: Consider the data presented below. Time  (s) 04080120160Moles of A0.1000.0670.0450.0300.020Determine whether the reaction is first order or second order.

###### FREE Expert Solution

We’re being asked to determine a reaction is first order or second order based on the data given.

Recall the first order and second order integrated rate law and their graph:

The integrated rate law for a first-order reaction is as follows:

$\overline{){\mathbf{ln}}{{\mathbf{\left[}}{\mathbf{A}}{\mathbf{\right]}}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{{\mathbf{\left[}}{\mathbf{A}}{\mathbf{\right]}}}_{{\mathbf{0}}}}$

where:

[A]t = concentration at time t
k = rate constant
t = time
[A]0 = initial concentration

The plot of ln [A] vs. t is linear which shows first-order reaction:

###### Problem Details
Consider the data presented below.

 Time  (s) 0 40 80 120 160 Moles of A 0.1 0.067 0.045 0.03 0.02

Determine whether the reaction is first order or second order.