How much energy (in kJ/mol) is released in the fusion reaction with 2H and 3He?

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insert step 1> Identify the fusion reaction: The fusion reaction involves deuterium (\(^2\text{H}\)) and helium-3 (\(^3\text{He}\)). The balanced chemical equation for this reaction is: \(^2\text{H} + ^3\text{He} \rightarrow ^4\text{He} + ^1\text{H}\).

insert step 2> Determine the mass defect: Calculate the mass of the reactants and the mass of the products. The mass defect is the difference between the total mass of the reactants and the total mass of the products.

insert step 3> Convert the mass defect to energy: Use Einstein's equation \(E = mc^2\) to convert the mass defect into energy. Here, \(m\) is the mass defect and \(c\) is the speed of light (\(3.00 \times 10^8\) m/s).

insert step 4> Convert the energy from joules to kilojoules: Since the energy calculated will be in joules, convert it to kilojoules by dividing by 1000.

insert step 5> Calculate the energy per mole: Use Avogadro's number (\(6.022 \times 10^{23}\) mol\(^{-1}\)) to convert the energy from per reaction to per mole. This will give you the energy released in kJ/mol.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Fusion

Nuclear fusion is a process where two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This reaction is the source of energy for stars, including the sun, and occurs under extreme temperature and pressure conditions. In the context of the question, the fusion of deuterium (2H) and helium-3 (3He) is a specific reaction that releases a significant amount of energy.

Energy Release in Reactions

The energy released during a nuclear fusion reaction can be quantified in terms of kilojoules per mole (kJ/mol). This energy is derived from the mass difference between the reactants and the products, as described by Einstein's equation E=mc². Understanding how to calculate this energy is crucial for determining the efficiency and feasibility of fusion as an energy source.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. In fusion reactions, the binding energy of the resulting nucleus is greater than that of the original nuclei, leading to the release of energy. This concept is essential for understanding why fusion reactions can produce energy and how the stability of nuclei affects the energy output.

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Textbook Question

What are the benefits of using fusion over fission as a source of nuclear energy? Why have fusion reactors not been developed yet?

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