Finding the least molar mass of organic compound having molar mass > 100

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SUMMARY

The discussion focuses on determining the least molar mass of an organic compound with a molar mass greater than 100, containing only carbon (C), hydrogen (H), and nitrogen (N). The percentage of carbon is six times that of hydrogen, and the sum of the percentages of carbon and hydrogen is 1.5 times the percentage of nitrogen. Through calculations, it is established that nitrogen constitutes 40% of the compound, leading to a system of equations that reveals multiple potential molecular formulas, from which the compound with the least molar mass must be identified.

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Homework Statement



In an organic compound of molar mass > 100 containing only C, H , N, the percentage of C is 6 times the percentage of H while the sum of the percentages of C and H is 1.5 times the percentage of N. What is the least molar mass?

Homework Equations



C% + N% + H%= 100%
therefore, 1.5N%+ N%= 100%

The Attempt at a Solution


From the above equation that I manage to calculate, N% should be 40%, the next step that I want to take is just not coming exactly to me, though I had a rough idea from the hints given in the question, but finally didn't actually manage to get the exact answer.
 
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Three unknowns, two equations.

Which means that you won't be able to solve this exactly. There won't be one unique solution to the percentages of the elements. It can stand for a variety of molecules, each with a different molar mass and HENCE the question asks you to go for the molecule with the least molecular mass.

1) Solve linear equations as much as you can
2) When you are done with the solving part, list out ALL possible molecules, you'll find a pattern to them and you'll find that they are many.
3) But the least one will stand out!
 

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