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8 How long does it take to exhale a Hamburger?

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Have you ever thought about where the weight goes when you lose weight? After studying metabolism you should have an idea now. The question we want to solve in this tutorial is how long it takes to exhale a Hamburger. This poses the first question:

Question 1: How do you exhale a Hamburger?

When we fully oxidise nutrients, we convert them into CO2 and H2O. For the protein content we also create urea (H2N-CO-NH2).

Before attempting the tutorial make a guess how long it will take to exhale a Hamburger (a Big Mac to be precise).

To solve the problem, you may use any online source you like including AI. Make sure that the information you get is reliable.

The next question is:

Question 2: How could you calculate this number?

1.Determine the amount of protein, fat and carbohydrates in a Big Mac.

2.Generate balanced equations for the full oxidation for each of the nutrients

3.Determine the total amount of CO2 generated by the complete oxidation of all nutrients in the Big Mac.

4.Determine the amount of CO2 exhaled/min by a person of your size.

5.Divide the total amount of CO2 generated from the Big Mac by the amount of CO2 exhaled/min.

Q3: How many calories does a Bic Mac have?

Q4: What is the content (in g) of a Big Mac of protein, carbohydrate and fat?

590kcal = 2472 kJ

  • Fat 34g,
  • Carbohydrates, 46g
  • Protein 25g

Q5: What are the balanced equations for the complete oxidation of carbohydrates, fat and protein?

2 C6H10O5 +12 O2 → 12CO2 + 10 H2O Please note that the oxidation of glucose follows the formula: C6H12O6 + 6O2 → 6CO2 + 6H2O but starch has the formula [C6H10O5]n

C55H104O6 + 78 O2 → 55 CO2 + 52 H2O

This is an average fat molecule the length of the fatty acids can vary.

C144H224N38O48S18 + 174.5 O2 → 125 CO2 + 74 H2O + 18 SO3 + 19 CO(NH2)2

This is an average protein.

Q6: how do you convert this into grams?

By calculating the molecular weight for a Mol of each molecule. Subsequently, setting the nutrient molecule to unity and calculating a weight ratio of the reaction. 

2 C6H10O5 +12 O2 → 12CO2 + 10 H2O

324g           384g        528g      180g

1g                 1.19g         1.63g      0.56g

C55H104O6 + 78 O2 → 55 CO2 + 52 H2O

860g           2496g      2420g        936g

    1                  2.9            2.81            1.09

C144H224N38O48S18 + 174.5 O2 → 125 CO2 + 74 H2O + 18 SO3 + 19 CO(NH2)2

3828g                           5584g       5500g        1332g     1440g         1140g

1                                          1.46          1.44            0.35        0.38             0.3

Q7: What are the ratios (g nutrient/g CO2) for each nutrient?

g nutrient: g CO2

Carbohydrates 1:1.63

Fat 1:2.81

Protein: 1:1.44

Q8: How many g CO2 have to be exhaled to remove all CO2 of the Big Mac from your body?

  • Carbohydrates, 46g x 1.63 = 75g
  • Fat 34g x 2.81 = 95.5g
  • Protein 25g x 1.44 = 36g

Total 75g + 95.5g + 36g = 206g CO2

Q9: What volume of CO2 has to be exhaled to get rid of the Big Mac?

1 Mol of ideal gas occupies 22.4 L. 206 g of CO2 (MW 44) is equivalent to 4.7 Mol. 4.7 x 22.4 = 105 L of CO2.

Q10: What is the fraction of CO2 in exhaled air?

Q11: How much air do you exhale per min?

There are about 4% CO2 in exhaled air.

While resting we exhale about 6L of air per minute.

Q12: How long does it take to exhale a Hamburger?

6 x 0.04 (Fraction of CO2) = 0.24L/min resting

105L/0.24L/min = 438 min = 7.3h

Q13: How does it change when you exercise?

The following table lists the exchange of CO2 in L/min under different conditions:

105L/0.24L/min = 438 min = 7.2h

105L/0.845L/min = 124 min = 2h

105L/1.48L/min = 71 min = 1h 20 min.

 

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