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Numerade Educator



Problem 16 Medium Difficulty

Calculate each of the following quantities:
(a) Mass (g) of $6.44 \times 10^{-2} \mathrm{mol}$ of $\mathrm{MnSO}_{4}$
(b) Amount (mol) of compound in 15.8 $\mathrm{kg}$ of $\mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}$
(c) Number of $\mathrm{N}$ atoms in 92.6 $\mathrm{mg}$ of $\mathrm{NH}_{4} \mathrm{NO}_{2}$


a) $\mathrm{m}=9,725 \mathrm{g}$
b) $\mathrm{n}\left(\mathrm{Fe}\left(\mathrm{ClO}_{4}\right)_{3}\right)=44,61 \mathrm{mol}$
c) $\mathrm{N}(\mathrm{N})=1,74^{*} 10^{21}$ atoms


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Video Transcript

When you're given a quantity either mass moles or Adams, it's helpful to create a road map where a plan to change from one to another they all are the same amount. They're just being measured in different units. If you have mass, you can change two moles by using the molar mass. Remember, the molar mass is found using the periodic table and the molar mass. The atomic masses, the number below each element. So to find the molar mass of anything, we simply add up the molar masses of those. So if you have mass and you want to go to moles, you divide by Moeller Mass. If you have moles and you want to go to Mass, you multiply by the molar mass. If, instead of looking at Mass, you're looking at atoms or molecules or particles we use of a God rose number. If you have Adams and you want to change to moules, you can divide by other Godric's numbers. If you have moles to Adams, you multiply by offer God rose number. You can also go from Masto Adams, or vice versa, always changing two moles first. So, for example, we have a certain amount of moles of a substance six point 44 times 10 to the minus tube nos of mn eso for we want to know how many grams that equals. We're starting at moles and changing to mass, so we need to multiply by the molar mass. So we have malls that we multiply my molar mass to get grams to find the molar mass. We use the periodic table, and we look up the molar mass of each substance. Do we have the mass of MN, which is 54 0.938 plus the mass of sulfur, which is 32.0 six? It was four times the mass of oxygen, and this gives us a total Mueller math of 151 2000 grams per mole. Where to find the equivalent, we multiply 6.44 times, 10 to the minus two nos. For every one mole, it is equal to 151.0 grams, so this has a mass of 9.72 grams. You could start instead with a mass. So, let's say, 15.8 kilograms of a substance F E Cielo for three and change it to moles. So if we have mass kilograms, we need to change it to mass in grams. And then we need to change two moles. And we do that by knowing that one kilogram is equal to 1000 grams. We use our Moeller Mass, so we have 15.8 kilograms. We change it to grams by multiplying by 1000 a man to change two moles we multiplied by the Moeller math. So one more, Um and using your periodic table, you find the molar mass of the substance to be 354 0.20 grams. So we take 15.8 times 1000 divided by 354.20 You find that it's equivalent to 44.6 mol Another example in which you have to be careful of looking at what the question is asking is if we have a certain mass of a substance. So 92.6 milligrams, uh, NH for ANO, too. And we want to know how many Adams of nitrogen are present in this compound. So we have a molecule and we're looking at the number of nitrogen atoms using the formula, so we'll start off with milligrams, which we have to change two grams. Once we have grams, we can change two moles. Once we have moles of our compound, we can change two molecules of the compound and then using the chemical formula, we can find the number of atoms of nitrogen. So to go from milligrams two grams, we know there are 1000 milligrams and everyone Graham from grams to moles will use the molar mass from moles to molecules we use of a god rose number. And then finally we used the chemical formula to see how many atoms there are in every molecule. So 92.6 milligrams for every one gram. There are 1000 milligrams. Using the periodic table, we find the molar mass and everyone mall of this substance has a molar mass of 92.6, 64 64 point 06 grams. Then every mole we know there are 6.2 times 10 to the 23rd molecules. And finally, if we look at the formula, there are two nitrogen atoms for every one molecule. So by multiplying 92.6 times 6.2 times 10 to the 23rd times two and then dividing by 1000 times 64.6 You see that there are 1.74 times 10 to the 21st Adams of nitrogen.