Final answer:
The energy released by the fusion of 1.00 kg of deuterium and tritium mixture can be calculated by determining the number of moles in 1.00 kg and then multiplying by the number of reactions to find the total energy. The average power output over a year is calculated by dividing the total energy by the number of seconds in a year.
Step-by-step explanation:
Calculating Energy from Fusion
The calculation of the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium involves several steps. The fusion reaction between deuterium (²H) and tritium (³H) releases 17.59 MeV of energy. Given the atomic mass of deuterium is 2.014102 u and tritium is 3.016049 u, the total mass per reaction is 5.032151 u. This equates to a molar mass of 5.03 g/mol for the reactants. Therefore, in a 1.00 kg mixture, there are approximately 198.8 moles of reactants.
Converting moles to the number of reactions, we have (198.8 mol) × (6.02 × 10²³ mol⁻¹) = 1.20 × 10²¶ reactions that take place. To find the total energy in joules, we multiply the energy per reaction by the number of reactions and convert MeV to joules (1 MeV = 1.602 × 10⁻¹³ J).
To determine the average power output over a year, we divide the total energy by the number of seconds in a year (31,536,000 seconds).