Recent work on the nuclear quadrupole resonance (NQR) investigation of molecular dynamics in the solid state has relied on 2D methods. We report our studies of dynamic processes by 1D shaped pulse NQR spectroscopy. Significant advantages include considerably shorter experimental duration, clear definition of the exchange time window, and avoidance of off-resonance effects. The reorientation of the Cl3C̃ group in polycrystalline chloral hydrate [Cl3C-CH(OH)2] is considered as a test case. This may be modelled as a three-site exchange process. An analysis of the generalised Bloch-McConnell equation is performed to formulate the kinetic matrix. The present approach involves simultaneous excitation of the sites that undergo chemical exchange by employing a suitably modulated shaped RF pulse, followed by a mixing time, and finally a suitable read pulse for signal detection. The experimental signal intensities are plotted against the mixing time to extract the kinetic parameters, i.e. the exchange rate and the spin-lattice relaxation rate. Variable temperature measurements are carried out to determine the activation parameters. Short experiment times are possible in our 1D mode, enabling a large number of runs to be readily performed as a function of mixing time and temperature. The kinetic and activation parameters obtained in the case of chloral hydrate are in good agreement with recent literature values.