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Problem 102 Medium Difficulty

Serotonin $(M=176 \mathrm{g} / \mathrm{mol})$ transmits nerve impulses between neurons. It contains $68.2 \% \mathrm{C}, 6.86 \% \mathrm{H}, 15.9 \% \mathrm{N},$ and 9.08$\% \mathrm{O}$ by mass. What is its molecular formula?


Molecular formula: $\mathrm{C}_{10} \mathrm{H}_{12} \mathrm{N}_{2} \mathrm{O}$


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Video Transcript

so we defend. Ah Tommaso Star Tony, Is this 1 76 comparable. And also the Master Standish of Calvin, 100 nitrogen and also all surgeons. So what would be the mark of the formula Social? Here we are going to find the actual, um, mess off cabin 100 nitrogen oxygen when we ha when we are using to move the mass. And then Ah, because from here we can also know that what were the mass off carpet in that? Overall 176 Quimper moves off for off the overall more the mass and also individual mass off. Uh, I mean, you devi the mass of individual elements, Okay. And then from there we can vow the lumber most, And that number most should be equals the number of carbons hydrogen, nitrogen and also union DeMarco from the Okay. So, um, first of all, we just need to found ah, correspond a massive carbon hydrogen nitrogen oxygen that dean the offer or mother mask. Okay, so we're going to do Ah, some mathematic. So we have a 1 76th time, zero points. Ah, I mean, 68.2% age. So we had one forever. 1 20 Graham. Four carbons and then for hydrogen. We have 176 times us. Ah, 6.86 home percentage. Eso We have reverence. 12.1 gram, and then we're doing the same thing for nitrogen. So if 15 for 9% time 176 Ah, we will have a 28 point. Oh, um, back Graham and then for oxygen. Ah, we're wants him a six time 9.8%. So we have lovely around 15.90 actually, are were actually, why up it would be 16. Um crap. Okay, so the next thing is, we're going to convert that to Longbourn rules. So for carbon, the lumber moves. Ah, we'll be equals to Ah, 10. Um, hydrogen will be with forever in 12 on Want ah, for nitrogen level forever into oxygen would be one. Ah, well, we're going to take the lumber most directly at as the number off individual Ah, atoms in the mark of the formula. So have seat hand age 12. We're going to just a whole one down to the whole number and sue and oh, So the molecule of formula forcible Tony would be seat and each 12 and sue Oh,