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Problem 118 Hard Difficulty

Solar winds composed of free protons, electrons, and $\alpha$ particles bombard Earth constantly, knocking gas molecules out of the atmosphere. In this way, Earth loses about 3.0 $\mathrm{kg}$ of matter per second. It is estimated that the atmosphere will be gone in about 50 billion years. Use this estimate to calculate (a) the mass (kg) of Earth's atmosphere and (b) the amount (mol) of nitrogen,
which makes up 75.5 mass $\%$ of the atmosphere.


a) $\mathrm{m}=4,73^{*} 10^{18} \mathrm{kg}$
b) $\mathrm{n}\left(\mathrm{N}_{2}\right)=1,27^{*} 10^{17} \mathrm{mol}$


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Video Transcript

we know the rate at which the mass of the earth is dissipating is three kilograms per second, and it's predicted that it will take 50 billion years for that all to decay so we can predict the math of the earth mass of the Earth by multiplying the rate times the time. We first need to change our time into second. So if I have 50 billion years, that's the same as 50 times 10 to the nine years. But I know there are 365 days and every year and 24 hours in a day and 60 minutes in an hour and 60 seconds in a minute. This is equivalent to 1.58 times 10 to the 18 second. So if it takes that much time for all of the earth to dissipate by multiplying that by the rate or three kilograms per second, we can predict the mass of the earth is 4.73 times 10 to the 18 kilograms. Second part of the question asked how much of that is nitrogen in moles and we know that it's the earth is 75.5% nitrogen so we start off with the mass of the earth, we can find the mass of nitrogen which we can then change two moles. We start by taking our initial mass of the earth and multiplying by the percentage and that will give us the mass of nitrogen and then to go from the massive from the massive nitrogen to the moles of nitrogen. We need the molar mass of end to and we find that using the periodic table one more is equal to two times the molar mass of nitrogen where one mole is 20 point Oh, won four grands. So if the mass of the earth this 4.73 times 10 to the 18 kilograms times 0.755 This tells us the amount of nitrogen in the earth is 3.57 I tend to the 18 kilograms. We have to change that two grams before we can change it to moles. When we do that by multiplying by 1000 or 3.57 times 10 to the 20 first grams and then our next step is to change two moles. Now we do this by dividing by the molar mass which equals 1.27 times 10 to the 20 moles