When we are performing IR spectroscopy for Cyclohexane and cyclohexene, we can distinguish them as cyclohexene has C-H carbon-hydrogen stretching so, it shows the absorption at 3000-2850 cm⁻¹ range, where the cyclohexane do not have this and it shows the -C=C- stretch at 1640-1680 cm⁻¹ range in the spectrum. So that is how we can distinguish both.
