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Chapter 3: Problem 103

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is the gas that is mainly responsible for global warming (the greenhouse effect). The burning of fossil fuels is a major cause of the increased concentration of \(\mathrm{CO}_{2}\) in the atmosphere. Carbon dioxide is also the end product of metabolism (see Example 3.13). Using glucose as an example of food, calculate the annual human production of \(\mathrm{CO}_{2}\) in grams, assuming that each person consumes \(5.0 \times 10^{2} \mathrm{~g}\) of glucose per day. The world's population is 6.5 billion, and there are 365 days in a year.

Short Answer

Expert verified
The annual human production of CO2, assuming each person consumes \(5.0 \times 10^{2} \mathrm{~g}\) of glucose per day, is approximately \(1.74 \times 10^{12} \mathrm{~kg}\) per year.

Step by step solution

01

Convert Mass of Glucose to Moles

First, convert the daily consumption of glucose to moles. The molar mass of glucose \(\left(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\right)\) is 180.156 g/mol. Therefore, using the conversion factor \(1 \mathrm{~moles} = 180.156 \mathrm{~g}\) of glucose, \(5.0 \times 10^{2} \mathrm{~g}\) of glucose is approximately \(2.775 \mathrm{~moles}\) of glucose.
02

Determine moles of CO2 produced from glucose

In the combustion of glucose, it produces 6 moles of CO2 for every 1 mole of glucose. So, multiply the number of moles of glucose, \(2.775 \mathrm{~moles}\) of glucose, by 6 to get the moles of CO2, which equals to \(16.65 \mathrm{~moles}\) of CO2 per person per day.
03

Convert moles of CO2 to grams

Convert the moles of CO2 produced per day to grams using the molar mass of CO2, which is approximately 44.01 g/mol. So, \(16.65 \mathrm{~moles}\) of CO2 is approximately \(732.66 \mathrm{~g}\) of CO2.
04

Determine annual production of CO2 per person and for the entire world population

Multiply the daily production of CO2, \(732.66 \mathrm{~g}\), by 365 days to get the total annual production of CO2 per person, which is approximately \(267,421 \mathrm{~g}\) or \(267.42 \mathrm{~kg}\) per person per year. To get the total CO2 produced by the entire world population, multiply \(267.421 \mathrm{~kg}\) by the world population of 6.5 billion. The result is approximately \(1.74 \times 10^{12} \mathrm{~kg}\) of CO2.

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Give an everyday example that illustrates the limiting reagent concept.

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