Question

The human body burns glucose (C6H₁2O6) for energy according to this chemical reaction:
CH₁2O6 +60₂-6CO₂ + 6H₂O
The products of the reaction are carbon dioxide (CO₂) and water (H₂O).
Interestingly, all of the carbon dioxide and much of the water exits the body through the lungs: on every breath, the average person exhales 500, mL of air,
which is typically enriched to 4% CO₂ and 5% water vapor by volume. In short, when a person loses weight by dieting, the weight that is lost actually departs
his body as a gas, every time he exhales. Each kilogram of body fat lost requires exhaling about 2.8 kg of carbon dioxide.
Calculate how many breaths it takes an average person to "exhale" 2.50 kg of fat. Round your answer to the nearest thousand.
You'll need to know that the density of CO₂ is 2.0 kg/m³.

Answer 1

Number of breaths required to burn 2.5 kg mass of fat is 175000 breaths.

What mass mass of carbon dioxide is in one breath?

The mass of carbon dioxide in one breath is calculated as follows:

• Mass = volume * density

Volume of Carbon dioxide in one breath = 4% * 500

Volume of Carbon dioxide in one breath = 20 mL = 2 * 10⁻⁵ m³

Density of carbon dioxide = 2.0 kg/m³

Mass of carbon dioxide in one breath =  2 * 10⁻⁵ m³ * 2.0 kg/m³

Mass of carbon dioxide in one breath =  4 * 10⁻⁵ kg

Mass of carbon dioxide to be exhaled to burn 2.5 kg of fat = 2.8 kg * 2.5 = 7 kg of carbon dioxide.

Number of breaths required = 7 kg/4 * 10⁻⁵ kg

Number of breaths required = 175000 breaths

In conclusion, the mass of carbon dioxide in one breath determines the number of breaths required to burn 2.5 kg of fat.

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