Final answer:
To calculate the change in internal energy (δE) for the combustion of a gas, subtract the work done on the surroundings from the heat absorbed or released. In this case, δE is equal to -166.5 kJ.
Step-by-step explanation:
To calculate the change in internal energy (δE) for the combustion of a gas, use the equation δE = q - w, where q is the heat absorbed or released by the system and w is the work done by or on the system. In this case, the gas releases 205 kJ of energy to its surroundings (q = -205 kJ) and does 38.5 kJ of work on its surroundings (w = -38.5 kJ). Thus, δE = -205 kJ - (-38.5 kJ) = -205 kJ + 38.5 kJ = -166.5 kJ. Therefore, the correct answer is (a) -166.5 kJ.