At the end of 2012, global population was about 7.0 billion people. 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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Welcome back everyone. 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 where one mole of glucose solid reacts with six moles of oxygen gas to produce six moles of carbon dioxide gas and two moles of liquid water. We have an entropy change for this reaction equal to negative 2,803 killed jules. We're told to calculate the mass of carbon dioxide and kilograms produced by the U. S. Population in 2021. If an average person consumes 2000 calories per day, let's recognize that. Based on the information given in the prompt, we're going to utilize geometry to solve this answer, we want to end up with our final units as kilograms of carbon dioxide for the mass. Let's begin with the figure given for the population As 332.9 times 10 to the six power people. We want to cancel out our unit of people. And we're going to utilize the conversion factor given in the last sentence of the prompt where we're told that an average person consumes 2000 calories per day. And so our numerator will be 2000 calories with a capital c. Where in our denominator will have people hyphen day And so we can cancel our units of people were left with calories per day and we can get rid of the unit day by multiplying by 365 days in one year. And so we just will have 365 days. So we won't have this as a fraction but we can cancel out days and we're left with calories in the numerator. Next we want to multiply by our conversion factor to cancel out calories. And just to be clear this should be a capital C for cal. So our next conversion factor comes from our textbooks and lecture where we would recall that one cow with a capital C is equivalent to 4.184 kg jewels. So canceling out cows were left with kilograms in the numerator. And next we will incorporate our conversion factor using our entropy and the relationship with carbon dioxide from our equation. And so recall that whenever we have storage geometry Calculations that involve entropy, we want to use the absolute value of our entropy and so it would be a positive value in that case. So in our denominator will plug in positive 2803 Killah jewels With the equivalence to c. 0 2 as six moles of C. 02 from our equation. So six moles of C. 02 is in our numerator. So canceling out killing jewels. Now we're left with moles of C. 02 in the numerator. And we want to multiply by our conversion factor to go from moles of C. 022 g of C. 02 for mass recall that we can utilize the molar mass from the periodic table for carbon dioxide which will see has a mass of 44 point oh one g equivalent to one mole of C. 02, canceling out multi C 02. We can finally get to our final unit being kilograms in the numerator of C. 02. And so in our denominator we want grams of c. 02 and we would recall that our prefix kilo tells us that we have 10 to the third power of our base unit. Graham canceling out grams were left with kilograms of C. 02 as our final unit. And in our calculators will find a result of 9.57873 times 10 to the 10th power kilograms of C 02 which we can round 236 fix as 9.57 times 10 to the 10th power kilograms as our final answer. Now, if we are asked for sig figs which we weren't in this case, but if we were, we would round based on the least precise measurement a K. A. The measurement with the least number of sig figs being 2000 calories per day, which only has one sig fig in our calculation being the two. And so we would round this 23 Sig figs or sorry to one Sig fig correction as a value of one times 10 to the 10th power kilograms of CO two for our mast. And so this would also be a appropriate answer based on precision being to one sig fig versus three Sig figs as our first highlighted answer. So what's highlighted in yellow? Are our answers to complete this example corresponding to choice A in the multiple choice? I hope this made sense and let us know if you have any questions.

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Key Concepts

Stoichiometry

Caloric Conversion

Thermochemistry