The metabolic oxidation of glucose, C6H12O6, in our bodies produces CO2, which is expelled from our lungs as a gas: C6H12O6(aq) + 6 O2(g) → 6 CO2(g) + 6 H2O(l). (a) Calculate the volume of dry CO2 produced at normal body temperature, 37 °C, and 101.33 kPa when 10.0 g of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at 100 kPa and 298 K, to completely oxidize 15.0 g of glucose.

Verified step by step guidance

Step 1: Calculate the moles of glucose (C6H12O6) consumed using its molar mass. The molar mass of glucose is approximately 180.18 g/mol. Use the formula: moles = mass / molar mass.

Step 2: Use the stoichiometry of the balanced chemical equation to determine the moles of CO2 produced. According to the equation, 1 mole of glucose produces 6 moles of CO2.

Step 3: Apply the ideal gas law to find the volume of CO2 produced at 37 °C and 101.33 kPa. The ideal gas law is PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant (8.314 J/(mol·K)), and T is temperature in Kelvin.

Step 4: For part (b), calculate the moles of glucose (C6H12O6) using its molar mass for 15.0 g of glucose. Again, use the formula: moles = mass / molar mass.

Step 5: Determine the moles of O2 required using the stoichiometry of the balanced equation, where 1 mole of glucose requires 6 moles of O2. Then, use the ideal gas law to calculate the volume of O2 needed at 100 kPa and 298 K.

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 relationships between the quantities of substances involved in a reaction. In this question, stoichiometry is essential for converting grams of glucose to moles and then using the mole ratios from the balanced equation to find the volumes of CO2 and O2 produced or required.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is crucial for calculating the volume of gases produced or consumed in a reaction under specific conditions. In this question, it will be used to find the volume of CO2 produced at body temperature and pressure, as well as the volume of O2 needed at different conditions.

Molar Volume of a Gas

The molar volume of a gas is the volume occupied by one mole of an ideal gas at standard temperature and pressure (STP), which is approximately 22.4 L at 0 °C and 1 atm. However, conditions can vary, so adjustments must be made for different temperatures and pressures. Understanding molar volume is important for converting moles of gas to volume, as required in the calculations for CO2 and O2 in this question.

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