Ch.5 - Thermochemistry

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.5 - Thermochemistry

Problem 97

Chapter 5, Problem 97

At the end of 2012, global population was about 7.0 billion people. What mass of glucose in kg would be needed to provide 1500 Cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to CO₂(𝑔) and H₂O(𝑙) according to the following thermochemical equation: C₆H₁₂O₆(s) + 6 O₂(𝑔) → 6 CO₂(𝑔) + 6 H₂O(𝑙) ΔH° = -2803 kJ

Verified step by step guidance

Calculate the total number of Calories needed for the global population for one year. Multiply the daily Caloric intake per person by the number of people and then by the number of days in a year.

Convert the total Caloric intake from Calories to kilojoules (kJ) knowing that 1 Calorie equals 4.184 kJ.

Use the thermochemical equation provided to determine the amount of energy produced by the combustion of glucose. Note that the combustion of one mole of glucose releases 2803 kJ.

Calculate the number of moles of glucose needed to meet the global energy requirement by dividing the total energy requirement (from step 2) by the energy released per mole of glucose (from step 3).

Convert the number of moles of glucose to mass in kilograms. Use the molar mass of glucose, which is approximately 180.16 g/mol, and convert grams to kilograms.

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Key Concepts

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

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of a substance needed or produced in a reaction. In this question, stoichiometry will help calculate how much glucose is required to meet the caloric needs of the global population by using the provided thermochemical equation.

Caloric Conversion

Caloric conversion involves translating energy requirements, typically measured in calories, into a mass of a specific substance. In this case, we need to convert the daily caloric needs of the population into a total annual requirement and then relate that to the energy released from glucose metabolism. Understanding this conversion is essential for determining the mass of glucose needed.

Thermochemistry

Thermochemistry is the study of the heat energy associated with chemical reactions. The given thermochemical equation provides the enthalpy change (ΔH°) for the metabolism of glucose, indicating how much energy is released when glucose is completely oxidized. This information is crucial for calculating how much glucose is necessary to provide the required energy for the global population.

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The heat of combustion of ethanol, C₂H₅OH(l), is -1367 kJ/mol. A bottle of stout (dark beer) contains up to 6.0% ethanol by mass. Assuming the density of the beer to be 1.0 g/mL, what is the caloric content due to the alcohol (ethanol) in a bottle of beer (500 mL)?

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Textbook Question

The standard enthalpies of formation of gaseous propyne (C₃H₄), propylene (C₃H₆), and propane (C₃H₈) are +185.4, +20.4, and -103.8 kJ/mol, respectively. (c) Which is the most efficient fuel in terms of heat evolved per unit mass?

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Textbook Question

It is interesting to compare the 'fuel value' of a hydrocarbon in a hypothetical world where oxygen is not the combustion agent. The enthalpy of formation of CF₄(g) is -679.9 kJ/mol. Which of the following two reactions is the more exothermic?

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(g)

CH₄(g) + 4 F₂(g) → CF₄(g) + 4 HF(g)

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Textbook Question

Consider a system consisting of the following apparatus, in which gas is confined in one flask and there is a vacuum in the other flask. The flasks are separated by a valve. Assume that the flasks are perfectly insulated and will not allow the flow of heat into or out of the flasks to the surroundings. When the valve is opened, gas flows from the filled flask to the evacuated one. (a) Is work performed during the expansion of the gas? (b) Why or why not?

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Textbook Question

The air bags that provide protection in automobiles in the event of an accident expand because of a rapid chemical reaction. From the viewpoint of the chemical reactants as the system, what do you expect for the signs of q and w in this process?

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