Question

The heat of combustion of fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), is \(-2812 \mathrm{~kJ} / \mathrm{mol}\). If a fresh golden delicious apple weighing \(4.23 \mathrm{oz}(120 \mathrm{~g})\) contains \(16.0 \mathrm{~g}\) of fructose, what caloric content does the fructose contribute to the apple?

Short answer

The fructose in the fresh golden apple contributes approximately -59.7 Cal to the caloric content of the apple.

Step-by-step solution

Convert the given mass of fructose to moles

To do this, we will need the molar mass of fructose (C6H12O6). We can obtain the molar mass by adding up the individual molar masses of the elements in fructose. The molar mass of Carbon (C) = 12.01 g/mol The molar mass of Hydrogen (H) = 1.01 g/mol The molar mass of Oxygen (O) = 16.00 g/mol Molar mass of fructose (C6H12O6) = (6 * 12.01) + (12 * 1.01) + (6 * 16.00) = 180.18 g/mol Now, we can convert the mass of fructose (16 g) in the apple to moles using the molar mass: moles of fructose = mass of fructose / molar mass of fructose = 16 g / 180.18 g/mol = 0.0888 mol

Calculate the energy produced during combustion of fructose

We can use the heat of combustion of fructose (-2812 kJ/mol) to find the energy produced for 0.0888 moles of fructose: Energy produced = moles of fructose * heat of combustion per mole Energy produced = 0.0888 mol * -2812 kJ/mol = -249.6 kJ (Note that the energy is negative because energy is released during combustion)

Convert the energy into calories

Since we need to find the caloric content of the fructose in the apple, we have to convert the energy from kilojoules to calories. We can use the conversion factor: 1 Cal (also known as food calorie or kilocalorie) = 4.184 kJ Caloric content = Energy produced / conversion factor Caloric content = -249.6 kJ / 4.184 kJ/Cal = -59.7 Cal

Report the caloric content of the fructose in the apple

The fructose in the fresh golden apple contributes approximately -59.7 Cal to the caloric content of the apple.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It provides the basis for balancing chemical equations, determining reaction yields, and calculating the amounts of reactants needed or products formed. In the context of the combustion of fructose, stoichiometry helps us understand the precise amount of fructose that is reacting and the energy released as a result.

For example, stoichiometry allows us to calculate the moles of fructose based on its mass and molar mass. Knowing the number of moles enables us to use the heat of combustion to find out the total energy released when the fructose is completely burned. This is an essential step in calculating the caloric content of foods, as it links the mass of a substance to its energy content.

Thermochemistry

Thermochemistry is the study of the heat energy involved in chemical reactions. When substances react, energy is either absorbed or released, and the measurement of this energy change is crucial in understanding the thermodynamic properties of a reaction. The heat of combustion is a thermochemical concept that quantifies the energy released when a compound undergoes complete combustion with oxygen under standard conditions.

In our example, the negative sign of the heat of combustion of fructose indicates that energy is released during the reaction, which is typical for exothermic reactions like combustion. The understanding of thermochemistry is essential in calculating the caloric content in food since it allows us to link the chemical energy stored in bonds to the thermal energy that can be utilized by organisms.

Molar Mass

The molar mass of a compound is the mass in grams of one mole of its molecules and is expressed in grams per mole (g/mol). It is a fundamental concept in stoichiometry as it provides a link between the mass of a substance and the number of its particles – atoms, molecules, or ions. To calculate the molar mass, we sum the atomic masses of all atoms in a single molecule of the compound.

In the case of fructose, the molar mass is critical for converting the 16.0 grams of fructose found in the apple into moles, which is a necessary step for using the heat of combustion to find the caloric content. Understanding how to calculate molar mass is a vital skill for accurately performing these conversions in chemistry.

Calorimetry

Calorimetry is a technique used to measure the amount of heat absorbed or evolved during a chemical or physical process. In biochemistry and nutrition, calorimetry is utilised to determine the energy content of foods, known as the caloric content. This is done by measuring the heat produced during a combustion reaction in a controlled environment, similar to the body's metabolism of food.

In our example, we use calorimetric data given as the heat of combustion to estimate the caloric content of fructose in an apple. By using stoichiometry to find the moles of fructose and then applying the energy per mole, we can calculate the total thermal energy in kilojoules and then convert it to food calories, which are the standard units for energy content in nutrition.