Carbon dioxide (CO2) is the gas that is mainly responsible...

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 Sample Problem 3.4). 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, that the world's population is 6.5 billion, and that there are 365 days in a year.

Key Concepts

Unit Conversion and Scaling

Unit conversion and scaling involve translating quantities from one set of units to another and scaling these calculations when moving from individual measurements to collective totals. This concept is critical in problems where daily consumption data must be extrapolated to an annual global scale, ensuring that the final result is expressed in the correct units.

Greenhouse Effect

The greenhouse effect refers to the trapping of heat in the Earth's atmosphere by greenhouse gases, such as carbon dioxide. This process leads to an increase in Earth's surface temperature and is a fundamental concept in understanding global warming and climate change.

Metabolic Production of CO2

In biological systems, the metabolism of nutrients like glucose results in the production of carbon dioxide as a byproduct. This concept connects human and animal physiology with chemical reactions, where carbon compounds are broken down to release energy, making it crucial for understanding the natural sources of CO2 in the atmosphere.

Chemical Reaction Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows for the calculation of the amount of products formed (such as CO2 from glucose metabolism) based on the given quantities of reactants, making it essential for solving problems related to chemical reactions in both biological and atmospheric contexts.

Transcript

00:01 For this problem, we want to find how many grams of co2 are produced per year by the entire human population, given that each person consumes 5 .10 to the 2 grams of glucose a day, and that the human population is 6 .5 billion.

00:22 So the first thing that we want to do is we want to relate this glucose sample to co2.

00:29 And so the first thing that we're going to have to do is we're going to have to run.

00:32 Write that chemical equation for the combustion reaction of that in order to find the multiple ratio of carbon dioxide to glucose.

00:41 So we know the chemical formula for glucose is c6, h12 -06.

00:48 You know that our reactant is going to be o2, and we know that our two products are going to be h -2 and co2.

00:56 Now we want to balance this.

00:57 So we first look to our first element, which is carbon.

01:00 We have six on the left, but only one on the right to make it balanced.

01:04 Put a six here, so i have six on both sides.

01:07 Now we look at the hydrogen.

01:09 We have 12 on the left, two on the right, so to make 12 on both sides, put a six there.

01:15 Now we look to the oxygen.

01:17 We have 6 oxygen from the h2o and 12 oxygen from the co2.

01:21 And we have 6 oxygen here on the left hand side from the glucose.

01:27 So we're missing 12 oxygen.

01:29 So to make up the 12 oxygen, i'm just going to put a 6 in front of the co2.

01:33 So we get that our final balanced chemical equation for the combustion of glucose is c6h1206 plus 602, yields 6h22 plus 6 co2.

01:49 So now we know that for every mole of glucose that we get 6 moles of co2, and that's going to be very important information when it comes to calculating our final answer.

02:00 So we know that 6 to 1 is our ratio.

02:07 We want to find the molar mass of glucose and the molar mass of co2, which are two main substances, so that we can do some basic calculations.

02:16 So let's do glucose first.

02:20 C6 h1206.

02:21 So we have six carbons, which is 12 .01.

02:26 And then we have 12 hydrogens, each of which are 1 .008.

02:31 And then finally, we have six oxygens, which are 16 .00...