We present a systematic analysis of the intracluster medium (ICM) in an X-ray flux limited sample of 45 galaxy clusters. Using archival ROSAT PSPC data and published ICM temperatures, we present best fit double and single beta model profiles and extract ICM central densities and radial distributions. We use numerical cluster simulations to estimate uncertainties for all measurements. We examine the ICM properties within the context of models of structure formation and galaxy feedback. We present best fit ICM mass-temperature MICM-TX relations for MICM calculated within R500 and 1Mpc. These relations exhibit small scatter (17%), providing evidence of regularity in large, X-ray flux limited cluster ensembles. The slope of the MICM-TX relation (at limiting radius R500) is steeper than the self-similar expectation by 4.3sigma. There is a mild dependence of ICM mass fraction fICM on TX; the clusters with ICM temperatures below 5keV have a lower mass fraction =0.160\pm0.008 than hotter clusters =0.212\pm0.006 (H0=50; 90% conf intervals). Our large, X-ray flux limited cluster sample provides no evidence for a more extended radial ICM distribution in low TX clusters down to the sample limit of 2.4keV. We find that density variations in simulated clusters cause MICM to be overestimated by 12%. We also use simulations to estimate an fICM depletion factor at R500. We use the bias corrected mean fICM within the hotter cluster subsample as a lower limit on the cluster baryon fraction. In combination with nucleosynthesis constraints this measure provides a firm upper limit on the density parameter for clustered matter Omega_M<0.36\pm0.01 (H0=50).

accepted on 12/15/98 for publication in ApJ, Latex, 26 pages, 9 figs, see also http://astro.uchicago.edu/home/web/mohr