A low molecular weight copolymer is provided comprising propylene and ethylene, wherein the low molecular weight copolymer has a softening point in the range of 90 to 140° C., wherein the low molecular weight copolymer has a needle penetration that is equal to y, wherein y is defined by the following formula: y≤−0.000000262249x6+0.000172031278x5−0.046669720165x4+6.701746779438x3−537.286013331959x2+22,802.983472587x−400,204.018086126 wherein x in the above formula is the softening point of the low molecular weight copolymer, and wherein the low molecular weight copolymer has a molecular weight polydispersity index of about 3 to about 25, a crystallinity of about 18% to about 30% measured by X-Ray diffraction, and a Brookfield viscosity in the range of about 1000 to about 4000 cp at 190° C. measured by ASTM D 3236. Adhesive compositions comprising the low molecular weight copolymer are also provided.