What is the significance of the kink in the [A] vs T graph for a 2nd order reaction? The 2nd order graph shows a bit of a kink, whereas the 1st order graph is smooth.


What is the significance of this kink, and why does it appear in only the 2nd order graph.
What is the significance of the numerical value at this kink? The graph below show it occurs at $[A]=1.5-2$.
There's no significance to the shape, that's simply how any graph of the form $y = 1/(c+x)$ looks like ($c$ being any constant you like).
Even if the supposed "kink" has some significance, there isn't any significance to the number, especially since the number depends on your system anyway (it's dependent on the value of your rate constant as well as the initial concentration).