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Problem 96

An organic compound was found to contain only $\mathrm{C}, \mathrm{H},$ and Cl. When a $1.50-\mathrm{g}$ sample of the compound was completely combusted in air, 3.52 $\mathrm{g}$ of $\mathrm{CO}_{2}$ was formed. In a separate experiment, the chlorine in a $1.00-\mathrm{g}$ sample of the compound was converted to 1.27 g of AgCl. Determine the empirical formula of the compound.

Answer

Emperical Formula $C_{6} H_{5} C l$

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## Discussion

## Video Transcript

So at first we will find the number ofthe malls off. See Oto which was formed, you know, from the compassion off one point five. Come on the sample. So the number of most off sealed too will be mass over molar mass of pseudo. So the mass of the Seattle who just produced as three point five program that man's don't who the number of most will be treatment five toe over the molar mass of carbon dioxide which is forty four point one Grandpa are more. And this will give us value off zero point zero eight more now since in one molecule of so what will we have? One atom of carbon. And that means one more of Soto will have one more of carbon. And on Syria, follow suit will have fancy rate all of carbon. That means the number of carbon in Soto will also means zero point zero eight more Now from here we can find a massive Soto on the mass of sea in the sea or two produced who shall be simply the number ofthe malls off see times the molar massive sea which is to a point one cramp Our mall and this will give us a well off zero point nine six gram. So this is the mass off, See, in the sort of produced that means this is also the mass ofthe sea in the sample off one point five gram since the carbon. So the amount ofthe carbon in Soto is the amount of carbon in the sample because, um, the complete compassion off the substance gives us thiss fellow of carbon that Ms on the complete compassion means that the amount of carbon and original sample is completely combusted. Tto give this much amount off carbon in Kyoto so we can assume that this's the amount of the whole Carmen, which is present in the original sample now, since we're given the amount ofthe glory in in one gram of sample For that reason, we will find the amount ofthe carbon in one gram of sample. So if one point five gram of sample contains point nine six grand off carbon, one point five grams simple contains, um, zero point nine six gram carbone. That means one gram of sample contain zero point nine six gram over one one five crumb, which will give us value off the syrup on six for Graham Carbon said This's the amount of carbon in one gram of simple. Now we find out the mass of chlorine in one room sample. So when one gram of the sample is ah converted toe age is hell are it is converted to one point two seven gram of Giselle. So to find out the mass ofthe seal just again just following the similar posters. First we'LL find out the number ofthe malls off edges seal produced. So the number of malls officials still produced will be the mass ofthe edges seal produced over the molar as off a chisel which is one forty three point three two Grandpa are more, and this will give us a value off zero point zero one more now again, since one molecule of edges sealed contents one including atem leicht minutes. One more offer. The sale will contain one mole off chlorine and point on matloff. Azusa will contain point over matloff sale. So the number of mall off chlorine will also mean the sirah point zero one mall. That means the mass ofthe chlorine in the diesel produced will be zero point zero one more times the molar mass off Taurean, which is thirty five point four five. Cramp our mall. You can give us the halo off zero point three one gram. So this is the amount ofthe amount of chlorine, which is former college is fun reproduced in the form off Aegis Shield. Um, that men's This is the amount ofthe glory in in the original sample off one gram. And now we know the amount of chlorine in one gram sample, and we know the amount ofthe carbon in one gram sample. From there, we can find the amount of hydrogen in one gram sample. So if we just write once again Ah, the amount ofthe dead risen in one gram sample will be one gram minus the sam off the carbon, which is zero point six four gram plus the sum off chlorine, which is zero point three one gram. And this will give us a well off zero point zero five gram. So this is the mass off. I'd risen in. I want to have some. But now we know the mass off each element which is present in one gram of a sample. Now we'LL find the number of malls for each element, so number of most ofthe carbon will be and the mass of carbon in one gram, which is zero point six program over the molar mass of carbon which is still upon on in cramp her morn. And this will give us a value off, um, zero point zero five more. Now we'LL find the number of malls off high treason, which will be the massive federales. In their point is hero five gram over the molar mass of head Rosen, which is one point or a cramp. Our mall, and it will give us a hello off zero point zero one more. Oh, no was thereupon zero five mall again and the number of malls off chlorine will be equal to the molar mass and the mass of growing in one gram, which is zero point three one gram over the molar mass of chlorine, which is thirty five point for five. Gramp are more and this will give us a bell off zero point zero one more. Now we know the number of malls off each element present in wonder. Example. Now we have to find out the simplest a whole number ratio of the Smalls and we will find that by simply ah just we'Ll just divide each number of moles by the smallest number of malls which is zero point zero one more So we'LL divide each number of malls by days to get the smallest the simplest hole number issue for each element. So the whole number ratios for carbon will be zero point zero five mall over zero point zero one more, which will give us a total of five Then similarly, the ratio of ride Rosen will be also zero point zero five more over zero point zero on mold which you'll also be fine. And for chlorine it will be zero point zero or more over zero point zero On wall we shall be called the one So the simplest hole number issue here with me five isto five minutes to one and that means the empirical formula for this substance with me See five h five o and this's them bigger formula. Oh, not or it is feel c five h five seal So this is them prigel formula for this substance

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