We demonstrate the ability to excite and monitor many whispering gallery modes (WGMs) of a microsphere resonator simultaneously in order to make broadband optical absorbance measurements. The 340 microm diameter microsphere is placed in a microfluidic channel. A hemispherical prism is used for coupling the WGMs into and out of the microsphere. The flat surface of the prism seals the microfluidic channel. The slight nonsphericity in the microsphere results in coupling to precessed modes whose emission is spatially separated from the reflected excitation light. The evanescent fields of the light trapped in WGMs interact with the surrounding environment. The change in transmission observed in the precessed modes is used to determine the absorbance of the surrounding environment. In contrast to our broadband optical absorbance measurements, previous WGM sensors have used only a single narrow mode to measure properties such as refractive index. With the microfluidic cell, we have measured the absorbance of solutions of dyes (lissamine green B, sunset yellow, orange G, and methylene blue), aromatic molecules (benzylamine and benzoic acid), and biological molecules (tryptophan, phenylalanine, tyrosine, and o-phospho-L-tyrosine) at visible and ultraviolet wavelengths. The microsphere surface was reacted with organosilane molecules to attach octadecyl groups, amino groups, and fluorogroups to the surface. Both electrostatic and hydrophobic interactions were observed between the analytes and the microsphere surface, as indicated by changes in the measured effective pathlength with different organosilanes. For a given analyte and coated microsphere, the pathlength measurement was repeatable within a few percent. Methylene blue dye had a very strong interaction with the surface and pathlengths of several centimeters were measured. Choosing an appropriate surface coating to interact with a specific analyte should result in the highest sensitivity detection.