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Problem 98

An element $X$ forms an iodide $\left(\mathrm{XI}_{3}\right)$ and a chloride $\left(\mathrm{XCl}_{3}\right) .$ The iodide is quantitatively converted to the chloride when
it is heated in a stream of chlorine:
$$2 \mathrm{XI}_{3}+3 \mathrm{Cl}_{2} \longrightarrow 2 \mathrm{XCl}_{3}+3 \mathrm{I}_{2}$$
If 0.5000 $\mathrm{g}$ of $\mathrm{XI}_{3}$ is treated with chlorine, 0.2360 $\mathrm{g}$ of $\mathrm{XCl}_{3}$ is obtained. (a) Calculate the atomic weight of the element X. (b) Identify the element X.

(a) 138.906
(b) Lanthanum, $L a$

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## Video Transcript

So from the equation here, you can see that two more off excite tree reacts to produce to matloff Excel Tree. So that means that one mole off exit tree will produce one more of XL three and any number of malls off except three will pose the same number of most ofthe exfiltrate. Now, if we ah consider not atomic weight off eggs as eggs. Then we had given a quantity off point five graham, except Tree is reacting to produce point two three six zero Graham Excel tree. So we can ride this amount of mass in terms ofthe number off malls like thiss. So the number of most for X I three will be equal to the massive Excite three, which is your plan five triples, zero graham over the molar mass off exit tree. So the more massive Except he will be, um, the sum of the atomic weight of X and I train. So the atomic weight off X class three times the atomic weight off out in. So the outing as that required off one twenty six point nine Graham and we have three out in. That's I will use. Multiply this by three so this will be the number of most for Exit three, and similarly, the number of balls off XL three will be equal to live two three, six zero graham over that weight off. Or the more massive Exhale Tree, which will be again the sum of the atomic weight off X glass three times the atomic weight off glory in which is thirty five point four five gram. And since from the balanced equation, we can see that the number of malls off except three is equal to the number of most ofthe axillary. That means vegan, right? This is equal to this. So that means number of all Self Excel tree will be called a number of months off. Excite three that men's home exurban toe through six year O gram over explain. No three times started five point four five is one or six point through. Fine is equal to zero point five triple zero gram over express three eighty points, seven gram And from there again, if we just cross multiply, we'LL have There are one two three six zero Graham Time's Explosive three eighty point seven Crumb equal to five triple zero gram times X plus one of six point through fame crumb. So from here we can find our just solving this equation. We can find out the value ofthe a X which will get as, um one thirty eight point nine zero Graham. So this is the etame Kuwait, off X and from the sacrum equate if we look for this atomic weight in the periodic table, you'LL see that this's that coming. Quit off, Lenton. Um, which has exactly same atomic weight off one. Thirty eight point nine so that we may assume it. So that week wait off exist one thirty eight one nine and no, The unknown element is lenton, um