This section supplements the discussion in Section 19.5 of the text on factors that govern the appearance of infrared spectra. It is also a supplement to Lab 2b, the IR Spectrum of Acetylene.
This page knows the correct vibration-rotation constants for the C2H2 spectrum you can measure in lab. It allows you to enter intital rotational numbers J'' and the spectrum branch, P or R (in which J changes by -1 or +1, respectively), of the transition, and it will calculate the transition energy. You may find this helpful as you assign your own C2H2 spectrum (but you're on your own with C2D2, and of course you should do your own analysis for C2H2 before turning here for confirmation).
The top figure shows a "stick figure" spectrum, and the bottom figure shows a close-up view of the spectrum spanning the P(3) through R(3) lines. You can explore the effects of H nuclear spin, gas sample temperature, and spectrometer resolution in these figures.
If you set the nuclear spin quantum number to a negative number, the spectra are calculated as if spin had no effect. Set I to zero or any integer or half-integer to see the real effects of spin symetry and the Pauli Exclusion Principle. In the stick figure, the red lines locate transitions with J'' = an even number (a +1 parity) and the blue lines locate odd J''.
Change the gas temperature to see the effects of rotational state population changes (and note how the Doppler width changes with T as well - it is a calculated result you shouldn't try to change). Change the spectrometer resolution to see the effects in the lower graph of instrumental effects. If you make the resolution too low, the spectral lines will be so narrow that they may not appear completely; this spectrum is calculated at only a finite number of points, and if the line is too narrow, it will be missed.