At the end of 2020, global population was about 7.8 billion. What mass of glucose in kg would be needed to provide 1500 Cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to CO₂(𝑔) and H₂O(𝑙) according to the following thermochemical equation: C₆H₁₂O₆(s) + 6 O₂(𝑔) → 6 CO₂(𝑔) + 6 H₂O(𝑙) ΔH° = -2803 kJ

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Hi everyone for this problem We're told the population of the us in 2021 was 332.9 million assuming that glucose is metabolized entirely to carbon dioxide and water according to the following equation We need to calculate the mass of carbon dioxide in kg produced by the US population in 2021. If an average person consumes 2000 calories per day. So let's figure out what it is that we want here. We want the mass of carbon dioxide in kilograms Produced by the US population in 2021. So that's where we're going to start. The problem tells us the population in 2021 it says that it's 332.9 million. So this number converted to an exponent is 332.9 times 10 to the 6th people. So we want to go from this number of people to mass of carbon dioxide in kilograms produced. Okay so let's start off by going from people to calories. They tell us that the average person Consumes 2000 calories per day. Okay so we can say that The conversion here because we want to first go from people to calories. So we want people to cross out so there's calories consumed per person per day. Okay so we'll say over people per day. Okay so now um are people cancels And we need our day to cancel because we want to go from people to calories. Okay so we need this day to cancel out here at the bottom. So we can multiply it by 365 days and this will be over one. Okay, so now our unit of day cancel. So now we have calories. So we want to go from calories to kilograms. But we can't directly go from calories two kg. But we can go from calories to kill a jules using that unit conversion. So in one calorie we have 4.184 kila jules. This wasn't given but it is something that we should know. One calorie has 4.184 kg jewels. So now our calories cancel. And we're in unit of killer jewels. Now, so now how can we go from kila jules, two moles of carbon dioxide. Let's look at our equation. So we have six moles of carbon dioxide and they give us the entropy they tell us that it is. So for every six moles of carbon dioxide We have 2, killah jewels of heat. So let's go ahead and use that unit conversion here. So for six moles of carbon dioxide we have kila jewels of heat. Okay, so now our killer jewels cancel. And we're in units of moles of carbon dioxide. The question asked us for The mass of carbon dioxide and kill a jewel. So we're almost there to go from moles of carbon dioxide 2g of carbon dioxide. We need to use the molar mass of carbon dioxide. So in one mall of carbon dioxide We have 44.01 g of carbon dioxide. And now we're in units of grams but it didn't ask us for it in grams. They asked us for it in kilograms. So the last thing we need to do is go from grams to kilograms And we know that in one kg there's 1000 g. Okay, so our grams cancel and you see we're left with kilograms. So this is going to give us our final answer which is 9.58 times 10 to the 10th kilograms of carbon dioxide. This is the mass of carbon dioxide produced by the US population in 2021. If the average person consumes 2000 calories per day, that's the end of this problem. I hope this was helpful.

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Key Concepts

Stoichiometry

Caloric Value of Glucose

Thermochemical Equations