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Numerade Educator



Problem 30 Medium Difficulty

The mineral galena is composed of lead(II) sulfide and has an average density of 7.46 $\mathrm{g} / \mathrm{cm}^{3} .$ (a) How many moles of lead(II) sulfide are in 1.00 $\mathrm{ft}^{3}$ of galena? (b) How many lead atoms are in 1.00 $\mathrm{dm}^{3}$ of galena?


a) $\mathrm{n}(\mathrm{PbS})=882,9 \mathrm{mol}$
b) $\mathrm{N}(\mathrm{Pb})=1,88^{*} 10^{25}$ atoms


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Video Transcript

when given a certain quantity of a substance to be changed into another substance. It's usually helpful to draw a visual diagram or a road map to show the conversions necessary. So, for example, if you know that you have a given volume or one cubic foot of a substance called lead two sulfide with a density of 7.46 grams per cubic centimeter, you can find out what this quantity is in moles. We're starting off with the volume. And so before we can find out how many moles we need to change that to mass when we do that, using the density once we have the mass, we can change two moles using the molar mass of the substance. So we're given the density in the problem. And before we start to do the conversions, we should change. Find the molar mass of lead two sulfide. So we have to figure out the formula this compound lead to meet the PB I on with a two plus charge and sulfide is s two minus. So the formula for this compound is P. B. S. Because for every positive there is a negative to find the molar mass of this compound we used. The atomic mass is given on the periodic table and add them up. So first we find the atomic mass for lead, which is 207 0.2 plus the atomic mass of sulfur 32.6 Those were both found on the periodic table, adding them together. One mole has a massive 239 quint, six grams great to six cramps that. So now we can do our conversions. Start off with a given quantity. One cubic foot. When we look at our density, we see the volume unit isn't centimeter, so we have to change it from the feet two centimeters. One foot is equal to 30 0.48 centimeters. Because it's a cubic foot, we need to cube the whole quantity. Do you eat cubic centimeters? We can then go to mass, using our density multiplying because we want the mass and that allows our cubic centimeters to cancel out. And then we know that one mole has a mass of 239.26 Gramps. So if we multiply 1.0 times 30.4 a cubed time 7.46 and divide by 239.26 We find this is equivalent to eat 183 moles of lead sulphide. We can look at a similar problem that finds not just moles but Adams. If we have a given volume in this case one cubic decimate er of the same compound with the same density we can find out how many atoms our present You start with volume in our roadmap which we changed him mass again using the density to get to Adams, we have to first go to moles from Mass. So we again use the molar mass. Once we have moles, we can go to molecules. We do this using of a god rose number because every mold contains the same number of out of molecules And finally to get to the number of atoms, we look at the ratio from the chemical formula. So again we start off in our conversion with are given volume one cubic decimate er because our density isn't centimeters. We need to change that to cubic centimeters in there 10 centimeters in one destiny eater to change it to cubic centimeters. We need to cube the entire quantity to change it to cubic Desam eaters for mass. We multiply by density 7.46 grams for everyone cubic centimeter, and then we go to moles using the molar mass we found above. One mole is equal to 239.26 grams for molecules. We know that one mole of any substance contains 6.2 times 10 to the 23rd units, which in this case, is a molecule. And finally, when we look at the ratio of lead Adams and lead molecules for every one molecule of lead sulfide, there's one lead Adam, because it's a 1 to 1 ratio, so multiplying 1.0 times 10 cube time, 7.46 times 6.2 times 10 to the 23rd and dividing it by the molar mass gives us 1.88 times tend to the 25th Adams of lead