For a specific work, on an average a person requires \(5616 \mathrm{~kJ}\) of energy. How many kilograms of glucose must be consumed if all the required energy has to be derived from glucose only? \(\Delta H\) for combustion of glucose is \(-2808 \mathrm{~kJ} \mathrm{~mol}^{-1}\). (a) \(0.720 \mathrm{~kg}\) (b) \(0.36 \mathrm{~kg}\) (c) \(0.18 \mathrm{~kg}\) (d) \(1.0 \mathrm{~kg}\)

Chemical thermodynamics is a branch of physical chemistry that deals with the relationship between heat energy and chemical energy, and the transfer of energy during chemical reactions. The key concept here is the enthalpy change \(\Delta H\), which is the total heat content of a system. In our exercise, the combustion of glucose is an exothermic reaction, which means it releases energy, indicated by a negative \(\Delta H\) value of -2808 kJ/mol.

An exothermic reaction like the combustion of glucose not only provides a source of energy but also reveals the amount of energy that can be derived from a substance. In a real-world context, this relates to how much energy our bodies can gain from consuming glucose — a critical aspect of metabolic processes.

In calculating the amount of glucose needed to fulfill a certain energy requirement, such as the 5616 kJ a person needs for specific work, we rely on the principle of conservation of energy. It's the thermodynamics that allows us to quantitatively connect the amount of a substance to the energy it provides or consumes.

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products involved in a chemical reaction. It's based on the balanced chemical equation and the law of conservation of mass. For the combustion of glucose, the stoichiometry allows us to directly relate the amount of substance (glucose) to the energy it releases when it reacts.

In the problem at hand, stoichiometry is used to determine how many moles of glucose are required to produce 5616 kJ of energy. By dividing the total energy requirement by the energy produced per mole of glucose, we get the stoichiometric ratio necessary to find the number of moles needed. This step is crucial because it bridges the gap between the abstract concepts of energy and the tangible mass of glucose that must be consumed.

Ratio Calculation

The formation of such ratios and their applications form the crux of stoichiometric computations. In essence, stoichiometry is the mathematical relationship between the elements in a reaction, both in terms of mass and energy, and is central to solving many real-life chemistry problems.

Molar mass calculation is fundamental in chemistry when converting between the mass of a substance and the number of moles. The molar mass is defined as the mass of one mole of a substance, usually in grams per mole (g/mol).

For glucose (C6H12O6), the molar mass is approximately 180.156 g/mol. The calculation involves adding up the atomic masses of all the atoms in one molecule of glucose. With this information, we can convert moles to grams, a step crucial for understanding the weight of glucose needed to meet the energy requirement.

To find the mass required for our energy needs, multiply the number of moles needed by the molar mass of glucose. This simple yet powerful calculation connects the concepts of stoichiometry and thermodynamics to provide a tangible solution to the problem – the exact mass of glucose that must be consumed.

Practical Applications

Calculating molar mass becomes highly relevant when dealing with dietary needs, pharmaceutical dosages, and chemical manufacturing processes, making it an invaluable tool in both lab settings and everyday life.