A 34.05 gram liquid sample of an unstable compound is deposited in a metal piston assembly that has a cylinder with a diameter of 20.0 cm. After the sample is added, the piston is placed in contact with the liquid and the piston vent is closed. This process removes all residual gas from the piston. The piston assembly is placed in 15.00 Kg of water at 30.00 oC. The barometric pressure is 778 mm Hg (760 mm Hg= 1 atm). As the compound spontaneously decomposes the piston moves up and the temperature of the water increases to 34.52oC. The piston rises 59.1 cm during the reaction. The contents of the cylinder at the end of the complete decomposition consists of 0.450 mol of carbon dioxide gas,0 .375 mol of liquid water, 0.0375 mol of oxygen gas and an unknown amount of gas from an unidentified element. Other useful information:

Question

∆Hfo CO2 = -393.5 Kj/mol

∆Hfo H2O = -286 kj/mol

Enthalpy of decomposition for unknown = -1893Kj/mol

Heat capacity of water = 4.184 J/goC

R = 0.08206 L x atm / mol x K or 8.3145 J/mol x K

Vapor pressure of H2O at 34.5oC = 41 mm Hg

Assume that the heat capacity of the piston assembly is negligible and the mass of the piston is negligible.