When eaten, dietary carbohydrates are digested to yield glu-cose (C6H12O6), which is then metabolized to yield carbon dioxide and water: Balance the equation, and calculate both the mass in grams and the volume in liters of the CO2 produced from 66.3 g of glucose, assuming that 1 mol of CO2 has a volume of 25.4 L at normal body temperature.
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insert step 1: Write the unbalanced chemical equation for the metabolism of glucose: C_6H_{12}O_6 + O_2 \rightarrow CO_2 + H_2O.
insert step 2: Balance the chemical equation by ensuring the number of atoms of each element is the same on both sides. Start by balancing carbon (C), then hydrogen (H), and finally oxygen (O).
insert step 3: Calculate the molar mass of glucose (C_6H_{12}O_6) using the atomic masses of carbon (C), hydrogen (H), and oxygen (O).
insert step 4: Convert the given mass of glucose (66.3 g) to moles using the molar mass calculated in the previous step.
insert step 5: Use the stoichiometry of the balanced equation to find the moles of CO_2 produced, then convert this to mass in grams and volume in liters using the given volume of 1 mol of CO_2 (25.4 L).
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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 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. Understanding stoichiometry is essential for determining how much carbon dioxide is produced from a given mass of glucose.
Balancing chemical equations involves ensuring that the number of atoms for each element is the same on both sides of the equation. This reflects the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. A balanced equation is crucial for accurate stoichiometric calculations, such as determining the amount of CO2 produced from glucose.
The volume of a gas at a given temperature and pressure can be related to the number of moles of the gas using the ideal gas law or specific molar volume values. In this context, knowing that 1 mole of CO2 occupies 25.4 L at normal body temperature allows for the conversion of moles of CO2 produced into a volume measurement. This relationship is key for calculating the volume of CO2 generated from the metabolism of glucose.
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