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Problem 46

Determine the empirical formula of each of the following compounds if a sample contains $(\mathbf{a})0.104 \mathrm{mol} \mathrm{K}, 0.052 \mathrm{mol}$ $\mathrm{C},$ and $0.156 \mathrm{mol} \mathrm{O} ;(\mathbf{b}) 5.28 \mathrm{g} \mathrm{Sn}$ and $3.37 \mathrm{g} \mathrm{F} ;(\mathbf{c}) 87.5 \% \mathrm{N}$ and 12.5$\% \mathrm{H}$ by mass.

Answer

a) $\mathrm{K} 2 \mathrm{CO} 3$

b) see explanation

c) $\mathrm{NH} 2(2$ is subscript)

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## Discussion

## Video Transcript

Okay, So in this problem, we have to find out the empirical formal of some gun bones. And we're given in first part of this problem, Orin. But if this problem were given the number ofthe malls off the elements, which ah composes the compound, and from here, we have to find out them pickle formal of the compound. So if we were given number ofthe most off each element, what we have to do is first, we have to divide each number of malls. Bye. The smallest number off more present here. And then those fellows we have to tow, um, make it to the nearest hole number. And that will be the ratio off each element present in the compound. And that, and from the Chris you we can find out them bigger formula of the Capone. So here we can see that on the smallest value is zero point zero five two. So we will divide all of the number of malls by this aeroplane zero five two on which will give us the ratio off the elements. Saturation off care. The Parisian here will be Zira. Plant one ofthe four mall over this zero point zero five two more And this will give us Obama off tool on the ratio. Carbone will be zero point zero five two over zero point zero five two which will be eventually won. And then the ratio of oxygen will be zero point one five six more over zero Plant zero five tumult. And this will give us value off three. So that means the ratio of guests he oh, is to his two. One is two three and that therefore, we can write the empirical formal of the components since we have to keep going, right, Get two, we have one serious. Then we get to see and then we have three oxy and you're right old three. So this is the M Brickell formal of the company Just scared to see or three. Then in the are built, this family were given the mass off um Daelim and switch makes up the compound. So what do you have to do? First, we'LL have to find out in the number ofthe malls for each element as they know that the number of false is equal to mass over Mollema. So we'll divide this mass is by their molar mass is to get the number of malls off each element and from them. Well, just follow the procedure we did in the previous problem. So this fight for and find out and the number of malls forage element first samosa off s and our teen will be mass off. This switches five point two eight gram over its smaller mass, which is one one hundred eighteen point seven one one point seven. Grandpa Armel, you give us a valuable off zero point zero for four Moeller. So for based accuracy foot is down. Here is for the molar mass. Four significant figures are taken as the molar mass off each element. So the number of most off Dean is Syria. Plant zero four four mall, which you have calculated here. Then we can create the most ofthe Floren, which will be the massive Florian three point three seven gram over its smaller mass which is eighteen point nine nine. Grandpa, our mole and this will give us a value off zero point one seven seven mole. Now we have the number of malls off, but the elements present in the compound now again, we have to divide this number off malls by the smallest Velo. So from Americans say that the smallest value is zero point zero four four. So you'LL divide this to number of moles by zero point zero four four to find out the ratio of fifteen and Floren in this compound. So what we'LL do is so Oh, the ratio off Tina will be equal to It's a number of multi jizz in urban, zero for four by zero point zero for four and forgive us well off one. And then the ratio of Florian will be, um zero plant one seven seven more, which is the number of months of Florin we calculated over the zero point zero four formal. And this will give us the value ofthe four point Oto and since it is very close to four, we can write it four. So the ratio off Essen and if here is one is two four that was the empirical formula will be since we wanna send right, Hasan and we have four Florin and for real grazes subscript off for if so then Brickell formal um, for dis comported sn F four. Now the next part of this problem, we have to find out. They bring a formal offer compound, which has eighty seven point five percent of nitrogen and clip on five percent of hydrogen. So when we're given percent as off the elements, what we'LL do first is will's sum up the person it is to make sure that the total is hundred percent and there is no other element present in the calm bone. So eighty seven point five percent plus twelve point five percent easily we can see that is totally one hundred percent. That meant in this compound on ly nitrogen and hydrogen represent and no other elements is present there. Now what we have to do is when a person is given, we will assume that the total mass of the A sample of this company's hundred grams That means this eighty seven point five percent will turn into eighty seven point five gram and twelve point five percent will turn into a twelve point five gram. And then again, we'LL just find out the number of moles for each element and then we will ah, we'LL divide those number of moles by the smallest fellow and from there will find out the ratio of the elements So let's find out the number of walls for some balls off nitrogen here is eighty seven point five gram, which is the mass of nitrous and in the sample overnight prisons Moler, Mus, which is fourteen point zero zero. And this is in Grandpa our mole. This will give us a value of six point two five more. This is the number of malls off nitrogen. Now we'LL find the number of most ofthe hide Rosen So massive hydrogen is dual planned five gram and mola Mazo treasonous One point or eight Grandpa are more. This will give us a well off jewel plant for Sara Moeller. So this is the number of months of Hydra and now we have to divide the number most by the smallest relevant. This policy is six point two five. That means the ratio off nitrous and will be six point two five more divided by six planned to five months. Give us a bell off one and the issue of high treason and will be to a point four zero mall over six point two five more. He was a fellow off one point nine eight. And since it's close toe too we can write it. Us too. So the ratio of nitrogen and hydrogen in this cos one is too, too. And that made them pickle. Formalize in H too. So this is the umbrella formula for the compound.

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