Sucrose (C12H22O11) is produced by plants as follows: 12 CO2(g) + 11 H2O(l) → C12H22O11 + 12 O2(g) H = 5645 kJ About 4.8 g of sucrose is produced per day per square meter of the earth's surface. The energy for this endothermic reaction is supplied by the sunlight. About 0.1 % of the sunlight that reaches the earth is used to produce sucrose. Calculate the total energy the sun supplies for each square meter of surface area. Give your answer in kilowatts per square meter 1kW/m2 where 1W = 1 J/s2.

Video transcript

Welcome back everyone. About .9 kg of carbon dioxide is produced per day per human. Assume that all of this carbon dioxide comes from the metabolism of glucose as shown below in the following reaction where solid glucose reacts with six moles of oxygen gas to form six moles of carbon dioxide gas and six moles of water. We have an entropy change for this reaction equal to negative 2803 kg per mole. And about 75% of this energy generated is used for daily basic functions, whereas 25% is used to maintain electric potential in cellular functions. We need to calculate the energy generated for daily basic functions in kilowatts based on the carbon dioxide produced per day. And so we're going to begin with the .9 kg of carbon dioxide which is produced per day per human. And we want to begin by converting from kilograms into grams per second of carbon dioxide. From here, we're then going to be able to go from grams per second to jules per second, where we would recall that one watt has an equivalence of one jewel per second. And that means that we can convert from jules per second to watts and then from watts to kilowatts for our final answer. So we're just using stoke eom a tree. And so we're going to follow that first conversion. Whereas we stated, we want to get two g per second. So we're going to multiply to go from kilograms in the denominator, two g of c 02 in the numerator where we would recall that our prefix kilo tells us we have 10 to the third power of our base unit graham, canceling out kilograms. We're now going to introduce time where we would say that one day in the numerator is equivalent to 24 hours in the denominator allowing us to cancel our unit of day. We have g per hour. We need g per second. So multiplying where we would recall that one hour in the numerator is equivalent to 60 minutes in our denominator. And then lastly we would get rid of hours where we go from. Or sorry, minutes where we go from one minute in the numerator with an equivalent of seconds in the denominator. And so canceling out hours as well as minutes were left with grams of carbon dioxide produced per second. And this will all simplify to a value of 0. g/s of carbon dioxide produced. Now with this value we can begin another calculation so we have 0.1416 g of c. 02 produced per second in which we want to get to jules per second. So multiplying to go from grams of carbon dioxide two moles of carbon dioxide. We want to recall our conversion factor being our molar mass for CO on the periodic table. Which One mole of co two is equal to 44. g of CO2. and so now canceling out g of co two. We can go from moles tequila jewels where we would note that based on our entropy change. This is for the entire reaction. But we know that energy Produced per human is in terms of carbon dioxide in the combustion of glucose. And so we would interpret this entropy change as kg of energy per six moles of carbon dioxide which comes from our balanced equation. And so that can be used as a conversion factor. Where we have again six moles of C. 02 in the denominator equal to 2803 killed joules of energy released. Since this is negative, meaning that this reaction is exo thermic. And so canceling out moles of C. 02. We now have killer joules per second in which we want to get to jules per second. So our last conversion factor has killed jules in the denominator and jewels in the numerator, where our prefix kilo tells us we have 10 to the third power of our base unit jewel canceling out killing jewels were left with joules per second. And this will simplify to a value in our calculators as 0.566 jewels per second of energy produced. Because we understand that One jewel per second is equivalent to one watt. We can therefore say that we have 110.566 watts of energy produced. And so now we can go from 110.5 66 watts and multiplied by the conversion factor to go from watts in the denominator, two kilowatts in the numerator where our prefix kilo tells us we have 10 to the third power of our base unit watt. So canceling out watts, we're left with kilowatts. And this will simplify to our final answer as zero point 110566 kW of Energy produced. And going back to the prompt. We need to get the energy generated only for daily basic functions in kW as our complete final answer. And so we know that 75% of energy generated is used for daily basic functions. So we can make note of that. So note that .75 Energy used for daily basic functions. And so we would say therefore we have our amount of energy produced. 0.1105 66 kilowatts multiplied by 660.75. And this gives us our final answer as 0.8 kilowatts of energy used for only daily basic functions. And so this will correspond to choice A and the multiple choice as our final answer. So I hope this made sense. And let us know if you have any questions