A 4.117 -g impure sample of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) was burned in a constant-volume calorimeter having a heat capacity of \(19.65 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). If the rise in temperature is \(3.134^{\circ} \mathrm{C},\) calculate the percent by mass of the glucose in the sample. Assume that the impurities are unaffected by the combustion process. See Appendix 2 for thermodynamic data.

Understanding the heat of combustion is fundamental in various scientific fields, particularly in thermochemistry. It refers to the amount of heat released when a substance is burned in the presence of oxygen. This heat is often measured using units of energy per substance mass, such as joules per gram (\(J/g\)) or units of energy per mole, such as kilojoules per mole (\(kJ/mol\)).

The heat of combustion is a critical parameter for fuels since it describes how much energy can be obtained from burning a unit mass of the fuel. In calorimetry, this value helps determine the energy content of different compounds and their purity. By burning a known mass of a compound and measuring the temperature change in a calorimeter, one can calculate the heat of combustion and, subsequently, the energy content of the sample.

In the given exercise, we measure the total heat release from the glucose combustion and relate it to the mass of glucose to determine its purity. This process involves multiple steps, from recording the temperature change in the calorimeter to calculating the percentage by mass of glucose.

Thermochemistry is a branch of chemistry that deals with the study of heat changes that occur during chemical reactions and changes in physical state. The first law of thermodynamics, which states that energy cannot be created or destroyed, underpins this field. This principle is crucial when measuring the energy changes in calorimetry experiments.

Calorimeters are devices specifically designed for measuring the heat of chemical reactions or physical changes, as well as heat capacity. The constant-volume calorimeter mentioned in the exercise is an apparatus where reactions take place at a constant volume, isolating the system from pressure changes and allowing for precise measurements of temperature changes which directly correlate with energy changes.

The temperature change measured in the calorimeter can be converted into heat using the calorimeter's known heat capacity, thus quantifying the thermochemical properties of the reaction, such as the heat of combustion for the glucose in the sample.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of moles, allowing chemists to predict the amounts of reactants needed and products formed in a reaction. In calorimetry, stoichiometry is essential in linking the amount of a substance to the heat released or absorbed during a chemical reaction.

In this context, the stoichiometric calculations involve using the molar mass of glucose to convert between grams and moles, so that the heat of combustion can be related to a standardized unit (per mole) and then applied to any given mass of the substance. By correctly applying stoichiometry, we ensure that the amount of heat measured is directly proportional to the mass of the reactant consumed, providing a clear and quantitative relationship between the two.

While solving the given exercise, stoichiometry plays a key role when we use the molecular weight of glucose to find the heat of combustion per gram, enabling us to correlate this to the actual heat measured, and ultimately determining the glucose's purity.

Percent composition refers to the percentage by mass of each element in a compound or the mass of a particular ingredient compared to the total mass of the mixture. It is important in chemistry to understand the makeup of compounds and mixtures, as well as in applications such as nutrition, pharmacy, and material science, where composition directly impacts performance and suitability.

In the context of the exercise, calculating the percent composition allows us to determine the purity of the glucose sample. After obtaining the actual mass of burned glucose from the calorimetry data, this mass is compared to the total mass of the sample to find the percentage by mass of glucose. The percent composition is particularly useful to assess whether the glucose sample contains the expected amount of glucose, or if there are impurities which can influence the results of experiments or the quality of the product.

Correctly determining the percent composition is crucial when quality control and specification of compounds are required, as in the pharmaceutical industry and various lab settings, to ensure that the results are reliable and standards are met.