Assume that an exhaled breath of air consists of 74.8% N₂, 15.3% O₂, 3.7% CO₂, and 6.2% water vapor. (c) How many grams of glucose (C₆H₁₂O₆) would need to be metabolized to produce this quantity of CO₂? (The chemical reaction is the same as that for combustion of C₆H₁₂O₆. See Section 3.2 and Problem 10.57.)

검증된 단계별 안내

Determine the total volume or mass of the exhaled breath to find the mass of CO₂ it contains. Assume a specific volume or use a typical value for a breath.

Calculate the mass of CO₂ in the exhaled breath using its percentage composition. Convert the percentage to a mass fraction and multiply by the total mass or volume of the breath.

Write the balanced chemical equation for the combustion of glucose, C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O.

Use stoichiometry to relate the moles of CO₂ produced to the moles of glucose consumed. From the balanced equation, 1 mole of glucose produces 6 moles of CO₂.

Calculate the mass of glucose needed by converting the moles of glucose to grams using the molar mass of glucose (180.16 g/mol).

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주요 개념

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Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this context, understanding stoichiometry is essential to determine how many grams of glucose are needed to produce a specific amount of carbon dioxide.

Combustion of Glucose

The combustion of glucose (C6H12O6) is a biochemical process where glucose reacts with oxygen to produce carbon dioxide and water, releasing energy. The balanced equation for this reaction is C6H12O6 + 6 O2 → 6 CO2 + 6 H2O. Knowing this reaction is crucial for calculating the amount of glucose required to generate a given quantity of CO2, as it directly relates the moles of glucose to the moles of CO2 produced.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. In this problem, calculating the molar mass of glucose will enable us to convert the moles of glucose needed to produce the specified amount of CO2 into grams.