The typical person needs a 2000 calorie diet to sustain “normal” activity. Nowadays, a lot of the energy in American diet comes from fats and sugars. Assume that “fats” provide 9.0 calories per gram and sugars (treat as glucose) provide 4.5 calories per gram. If your “typical” person got 25 % of their energy from fats and the other 75 % from sugar, then how many grams of oxygen per day would your typical person have to consume to convert the food into carbon dioxide and water? Assume “fats” are neutral triglycerides (C57H114O6) and assume sugars are all glucose (C6H12O6).There is a 5% error interval around the correct answer. The units are grams.
2000 x 0.25 = 500 calories from fat.
2000 x 0.75 = 1500 calories from sugar.
g fat x 9.0 cal/g = 500
g fat = about 55.6 g fat for 25%.
g sugar x 4.5 cal/g = 1500
g sugar = 333.3 g sugar for 75%.
g O2 needed for fat consumption is
2C57H114O6 x 165O2 = 114CO2 + 114H2O
mols fat = g/molar mass = about 55.6/895.5 = about 0.062
Convert to mols O2.
0.062 mols fat x (165 mols O2/2 mol fat) = about about 5 mols O2 which is 5*32 or 160 g oxygen needed to burn the fat.
g O2 needed for sugar consumption is
C6H12O6 + 6O2 --> 6CO2 + 6H2O
mols sugar = grams/molar mass = about 333/180 = about 1.85 mols sugar.
Convert to mols O2 then to grams O2.
1.85 mols sugar x (6 mols O2/1 mol sugar) = 11 mols O2 or 355 g oxygen for the sugar consumption.
Total oxygen needed = 355g for sugar + 160 g for fat = ?
Note that I've estimated here and there so you should go through and work the problem more accurately.
To determine the number of grams of oxygen required to convert the food into carbon dioxide and water, we need to calculate the moles of fats and sugars consumed, and then use the balanced chemical equation for the breakdown of these substances.
First, let's calculate the number of calories consumed from fats and sugars.
Assuming a 2000 calorie diet:
- 25% of the energy comes from fats: 0.25 * 2000 = 500 calories
- 75% of the energy comes from sugars: 0.75 * 2000 = 1500 calories
Now, let's convert the calories of fats and sugars to grams using their respective calorie to gram conversions.
- Fats provide 9.0 calories per gram, so the grams of fats consumed will be: 500 calories / 9.0 calories per gram = 55.56 grams (approximately)
- Sugars provide 4.5 calories per gram, so the grams of sugars consumed will be: 1500 calories / 4.5 calories per gram = 333.33 grams (approximately)
Next, let's calculate the number of moles of fats and sugars consumed.
- For fats (C57H114O6), we need to determine the number of moles of carbon, hydrogen, and oxygen present in the given formula. Then divide the grams of fats consumed by the molar mass to get the moles.
- Carbon: 57 g/mol
- Hydrogen: 114 g/mol
- Oxygen: 6 g/mol
- Molar mass of fats (C57H114O6) = (57 * C) + (114 * H) + (6 * O) = 57 * 12.01 + 114 * 1.01 + 6 * 16.00 = 845.18 g/mol
- Moles of fats consumed = 55.56 grams / 845.18 g/mol = 0.0658 moles (approximately)
- For sugars (C6H12O6), we simply divide the grams of sugars consumed by the molar mass to get the moles.
- Molar mass of sugars (C6H12O6) = (6 * C) + (12 * H) + (6 * O) = 6 * 12.01 + 12 * 1.01 + 6 * 16.00 = 180.16 g/mol
- Moles of sugars consumed = 333.33 grams / 180.16 g/mol = 1.8503 moles (approximately)
Finally, let's use the balanced equation for the breakdown of fats and sugars to calculate the grams of oxygen required per day.
1 mole of fats (C57H114O6) reacts with 80 moles of oxygen (O2) to produce 57 moles of carbon dioxide (CO2) and 57 moles of water (H2O).
1 mole of sugars (C6H12O6) reacts with 6 moles of oxygen (O2) to produce 6 moles of carbon dioxide (CO2) and 6 moles of water (H2O).
Using the moles of fats and sugars consumed, we can calculate the grams of oxygen required.
- For fats:
- Moles of oxygen needed = 0.0658 moles * 80 moles of O2 = 5.26 moles (approximately)
- Grams of oxygen needed = 5.26 moles * 32 g/mol = 168.32 grams (approximately)
- For sugars:
- Moles of oxygen needed = 1.8503 moles * 6 moles of O2 = 11.10 moles (approximately)
- Grams of oxygen needed = 11.10 moles * 32 g/mol = 355.17 grams (approximately)
Therefore, the typical person would need to consume approximately 168.32 grams of oxygen per day to convert fats and approximately 355.17 grams of oxygen per day to convert sugars into carbon dioxide and water.