Rapid passage signals showing the effects of molecular alignment have been observed when low pressure samples of nitrous oxide are interrogated by radiation from a pulsed 7.84 mu m quantum cascade laser. These effects occur when the sweep rate of the laser through a Doppler broadened absorption line is much faster than the collisional relaxation time, and when the power density of the linearly polarized laser radiation is sufficient to cause optical pumping. Using a laser pulse of duration 1.3 mu s, the frequency sweeps approximately 90 GHz. The variation of the laser tuning rate during the laser pulse, from about 100 MHz/ns at the beginning to about 20 MHz/ns at the end, allows the relationship between sweep rate and collisional damping to be investigated. It is shown, by comparing the experimental signals with those calculated by coupled Maxwell-Bloch equations, how the rapid passage effects in nitrous oxide are influenced by the number density, transition cross-section and reorientation lifetime.