We have analyzed the clumpy structure of the moderately dense, n(H2) similar or equal to 10(3) cm(-3) gas traced by the J = 1-0 lines of CO and (CO)-C-13 in the Rosette Molecular Cloud using Clumpfind, our automatic clump finding algorithm. About half of the clumps are gravitationally bound; about 15% are virialized. The clumps that are not gravitationally bound appear to be bound by the pressure of the interclump medium, which is largely atomic. The clumps in which star formation is known to be taking place tend to be the most massive clumps in the complex and are all virialized or very close to it. Column density profiles of the star-forming clumps are steeper than for the pressure-bound clumps, and are reasonably well described by a form rho(r) proportional to r(-2). The clump mass spectrum follows a power law, dN/dM proportional to M(-1.27) Similar to other giant molecular clouds (GMCs). We argue that the mass spectrum of the clumps does not evolve into the stellar IMF, which originates instead within the individual clumps. The internal density of the clumps measured by (CO)-C-13 is found to be nearly independent of clump mass. The volume filling fraction of the clumps relative to the entire GMC is 8%; the mean density contrast between the clump and interclump gas is about 40. Column densities are determined using the LTE method, but we find that to achieve consistency between the mass determined from (CO)-C-13 and the commonly used method using CO alone requires either that X = N-H2/W-CO = 1.1 x 10(20) cm(-2) (K km s(-1))(-1), or that N-H2 - 1.0 x 10(6) N-13CO. We favor the former alternative because the cloud does not appear virialized and because the resulting mass agrees better with the dynamical mass of the cloud. We show that the mass of the cloud can be determined well from the (CO)-C-13 alone and that N-13CO/W-13CO = 1.5 X 10(15) cm(-2) (K km s(-1))(-1). The clumps exhibit a gradient in velocity of 0.08 km s(-1) pc(-1) over the face of the cloud complex. If interpreted as rotation, then the rotational energy is a small fraction of the clump kinetic energy, 6%/sin(2) i, where i is the inclination of the rotational axis to our line of sight. The clump-to-clump velocity dispersion decreases with clump mass, sigma(v)(c - c) proportional to M(-0.15), indicating that the clump ensemble is dynamically evolved, but the system is far from equipartition and most of the kinetic energy of the cloud resides in the random motions of the largest clumps, T proportional to M(0.4). An additional sign of the evolutionary state of the cloud is that the most massive clumps lie closest to the midplane of the complex. It is shown that clumps that are closer to the Rosette Nebula show greater levels of star formation activity than similar clumps further away. There are also gradients in clump excitation temperatures and mean densities with distance to the H II region. We discuss the implications of these observations for the formation of the molecular cloud from an atomic cloud, the evolution of the clump mass spectrum, and the formation of stars.
