Calculate the mass of octane, C8H18, that must be burned in air to evolve the same quantity of energy as produced by the fusion of 1.0 g of hydrogen in the following fusion reaction: 4 1^1H → 4 2He + 2 0^1e. Assume that all the products of the combustion of octane are in their gas phases. Use data from Exercise 21.50, Appendix C, and the inside covers of the text. The standard enthalpy of formation of octane is -250.1 kJ/mol.

A combustion reaction is a chemical process in which a substance (typically a hydrocarbon) reacts with oxygen to produce carbon dioxide, water, and energy. In this case, octane (C8H18) combusts in air, releasing energy that can be quantified using its standard enthalpy of formation. Understanding the stoichiometry of the combustion reaction is essential for calculating the mass of octane needed to match the energy produced by another reaction.

The enthalpy of formation is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. For octane, the standard enthalpy of formation is given as -250.1 kJ/mol, indicating that energy is released when octane is formed. This value is crucial for calculating the energy released during combustion, which is necessary to determine how much octane must be burned to match the energy from the fusion of hydrogen.

The energy released during nuclear fusion, such as the fusion of hydrogen into helium, is significantly greater than that from chemical reactions. In the given fusion reaction, 4 hydrogen nuclei combine to form helium, releasing a substantial amount of energy. To solve the problem, one must first calculate the energy produced from the fusion of 1.0 g of hydrogen and then relate this to the energy released from the combustion of octane to find the required mass.