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Problem 48

Determine the empirical formulas of the compounds with the following compositions by mass:
$$\begin{array}{l}{\text { (a) } 55.3 \% \mathrm{K}, 14.6 \% \mathrm{P}, \text { and } 30.1 \% \mathrm{O}} \\ {\text { (b) } 24.5 \% \mathrm{Na}, 14.9 \% \mathrm{Si}, \text { and } 60.6 \% \mathrm{F}} \\ {\text { (c) } 62.1 \% \mathrm{C}, 5.21 \% \mathrm{H}, 12.1 \% \mathrm{N}, \text { and the remainder O }}\end{array}$$

a) See explanation for solution.
b) See explanation for solution.
c) See explanation for solution.

## Discussion

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## Video Transcript

So in this problem, we have to find out them picker formal off you compounds were given it so in their funerals to find out the empirical formula off a compound from the person does office elements. So these are the rules. So first rule here is we assume that in the compound has a mass off hundred rum, and in that case, the person off each element will turn into the mass off each element. And from those messes, we'LL find out the number ofthe malls off each element. And as they know that the number of most of an element is simply the mass over smaller mass. And while entering while using the molar mass or atomic mass, four significant figures are used. Tto mess the position off the experiment of messes. And then, finally, the simplest hole number issue of those number off moles R off calculated by simply dividing each number of moles. Bye. The smallest number off mole. So that means that well, we will divide each number off malls calculated by the smallest number of malls to find a smallest, the simplest whole number ratios off the number of malls and from the simplest precio. We can easily find out them pretty informal of the compound. So that started this first problem here. So here we have fifty three, fifty five point three percent gay for advances person B and then thirty one one percent O. So first, you have to make sure that the total of these three hundred percent and if we just some this three up we'LL see that the total is hundred percent that there is no other element in this compound. So, as you have said the recording the first rule, we will consider that total mess as hundred creme. That means this person has values will turn in tow Graham Mass fellows. So that means we have fifty five point three grams game, fourteen point six grumpy and thirty point one room open. So from this values, you can find out the number of most off each element present. So most ofthe care, the partition will be equal to fifty five point three grams over the molar mass operation, which is a thirty nine point one zero Grandpa Ramon, and this will give us a value off one plant for one more and similarly we can find out the mall's ofthe year for us, for us. So first for us to develop for important six gram and the Mormons off us for us is thirty point nine seven. So this will give us a value off zero point four seven one more, Same way Confined the number of months off oxygen to the massive vaccinia is thirty point one graham and the molar mass of oxygen is sixteen point zero. Grandpa, Our mall, this really was well off one point eight eight mole. So now, using the second rule, what we'LL do is we will, um, divide each number of moles by the smallest number of malls to find the simplest ratio off the elements. So from Americans, see that the smallest number is thiss So we'LL divide each number of malls by this point foursome and one which will give us a ratio of the elements present in the compound. So the issue off Kay will be one point for one more over zero point four seven one mole. It will give us ever hello off two point nine nine. And since it is very close to three, we can write it as three, then for force for us. Their issue will be zero pond force. When one mall over zero point four seven one mall, you have no form. And then for oxygen, there issue will be one point eight eight more over zero point four seven. One more And this would give us and fellow off three point nine nine and which we can write us for. So the ratio off potassium force for us and oxygen here our trees to one is to four. So then pickle formula for this company will be get three b o four. So this is them bigger formula for this company. Now, In the second part of this problem, we have twenty five percent sodium, fourteen by nine percent. Silicon insisted, wants his person Floren. So again will ah, consider this person is as Graham And then we calculate the number of malls for each atom. Our element. So for sodium it will be twenty four point five. Graem oversaw Williams Moler, Mass, which is twenty two point nine nine Graham are more. Give us the value ofthe one point all six more Then we'LL find out number of malls off silicon So the mass of silicon here is fourteen point nine Graham and we have silicon smaller mouths which is twenty eight point oid Graham, far more. And this will give us a value off zero point five. Three more nineteen nineteen and grandpa are more and this will give us a fellow off three point one nine more. Now we will divide each number balls by the smallest number, which is zero point five three. So that will give us the ratio of which elements The issue of sodium will be one point all six over zero point five three, which is a round figure off too. Then for silicon it will be zero point five three over zero point five three. Give us one and for Floren Bay three point one nine over zero point five three give us a value off six point oto are making it approximately six. So their issue here is two is two, one is two six and that means them pickle formal will be in a tow is I have six. So this is them brittle formula for the compound Now in the tart bard we're given person does off carbon hydro's and nitrogen and we're saying that the rest are in the remaining oxygen safely. Subtract the total from hundred sixty two point one for US five point two one plus twelve point one. We will find that, um, the wrist is twenty point five three. So this is the percentage off oxygen. And now again, we'LL just simply count. Each percent is as massing Graham and we'LL find the number ofthe malls for each element. Symbols for carbon will be sixty two point one gram over carbon smaller mass, which is to a point one well. Give us a value off five point one seven mall and then for night rose, and it will be to have one, one says at the party is twelve point one overnight lows in smaller muss, which is fourteen point zero zero, and it will give us a fellow off zero point eight six more They're planned. It's a small then for Hydra zin. The mass is five point two one and the molar mas's one point or eat gram bar more, and this will give us value off five point one seven more. And for oxygen, the masses twenty point five three over oxygen. Smaller mass, which is sixteen part serial Gramp our mall And this will give us a value off one point two eight more So and now ammo This four number of malls you can see that zero point eight six is the smallest. Now we'LL divide each fellow with zero point six to get the simplest ratio. So the issue of Carmen will mean five point one seven over zero point eight six. This will give us a fellow off six point zero one and we can write it six. Then for Hydra Zin it will be again Same five point one seven over zero point eight six which is six month one are approximately six. Then for nitro zin it will be him zero point eight six over zero point eight six She'LL be one and for OCS isn't it will be one point two eight over zero point eight six and it'LL give us a well off one point five. So now we can see that we have got three person it round figures But in this case it is, um just how far it through one and two That means we I cannot around it the one or two So to make it a round figure, the smallest her own figure we can make from his three. And for that we have to multiply this by two multiplied by multiplying by tool, you can get three. But in that case, we'LL have to multiply each number by two. So we multiplied this six pay to get twelve six six multiplied by two when he was twelve. And for nitrogen it'Ll be one time to go to two. Ooh! So the ratio off carbon, hydrogen and nitrogen and oxygen here is twelve is to twelve isto twisted three And that man's the empirical formal will be C two of each to have into or three. So this is the empirical formal, um, for that compound.