We introduce a method that addresses the elusive local density at the solute in the highly compressible regime of a supercritical fluid. Experimentally, the red shift of the pyrazine n-pi* electronic transition was measured at infinite dilution in supercritical ethane as a function of pressure from 0 to about 3000 psia at two temperatures, one close (35.0 degrees C) to the critical temperature and the other remote (55.0 degrees C). Computationally, stationary points were located on the potential surfaces for pyrazine and one, two, three, and four ethanes at the MP2/6-311++G(d,p) level. The vertical n-pi* (B-1(3u)) transition energies were computed for each of these geometries with a TDDFT/B3LYP/6-311++G(d,p) method. The combination of experiment and computation allows prediction of supercritical ethane bulk densities at which the pyrazine primary solvation shell contains an average of one, two, three, and four ethane molecules. These density predictions were achieved by graphical superposition of calculated shifts on the experimental shift versus density curves for 35.0 and 55.0 degrees C. Predicted densities are 0.0635, 0.0875, and 0.0915 g cm(-3) for average pyrazine primary solvation shell occupancy by one, two, and three ethanes at both 35.0 and 55.0 degrees C. Predicted densities are 0.129 and 0.150 g cm(-3) for occupancy by four ethanes at 35.0 and 55.0 degrees C, respectively. An alternative approach, designed to "average geometry specific shifts, is based on the relationship Delta nu = -23.9n cm(-1), where n = ethane number. out" Graphical treatment gives alternative predicted densities of 0.0490, 0.0844, and 0.120 g cm(-1) for average pyrazine primary solvation shell occupancy by one, two, and three ethanes at both 35.0 and 55.0 degrees C, and densities of 0.148 and 0.174 g cm(-3) for occupancy by four ethanes at 35.0 and 55.0 degrees C, respectively.