An optically coupled vibrating tube densimeter has been used to measure the relative densities of aqueous solutions of L-alanine and sodium bromide in the ranges 397 less than or equal to T/K less than or equal to 521 and 10 less than or equal to p/MPa less than or equal to 30. For the solute L-alanine, the reported relative densities have been used to calculate apparent molar volumes which, in turn, have been used in the calculation of partial molar volumes at infinite dilution. The latter data are modeled using an equation of state of the type reported by Helgeson, Kirkham, and Flowers. This model is compared to those recently reported by Clarke and Tremaine. The reported model for the temperature and pressure dependence of the apparent molar volume of L-alanine in water is used to derive expressions for the apparent molar compressibilty and expansibility of this system. Calculated data for the latter property are compared to those available in the literature. In addition, the partial molar volume at infinite dilution for the alanine side chain is calculated by combining the volumetric results reported in this manuscript for aqueous L-alanine solutions with those previously reported for aqueous solutions of glycine. Volumetric results for aqueous sodium bromide solutions have been compared to those calculated from a program by Archer that, utilizes the Pitzer Ion Interaction approach.