In a $\pu{45.9 g}$ sample of borane, a compound containing only boron and hydrogen, that's $85.63\%$ boron, what is the mass of hydrogen in this sample?

I was just going to take $\pu{45.9 g}$ and multiply by $0.1437$ to get the mass of hydrogen, but I don't think it works that way because they don't equally contribute to the mass of the compound. Then I thought, maybe I should consider the molar masses of both atoms, hydrogen being $\pu{1.008 g mol-1}$ and boron being $\pu{10.811 g mol-1}$. I am stuck at this point. How to solve the question.


The problem does not need any difficult approach, not even relative atomic masses, if you trust the one who made this exercise. Since borane (whatever type it is)* consists (by exercise's hypothesis) only of hydrogen and boron and since boron is $85.63\%$ by mass, hydrogen's mass percentage would be the remaining $100\% - 85.63\% = 14.37\%$. Therefore, we have $\pu{6.60 g}$ of hydrogen in this sample.

The compound borane, $\ce{BH3}$, is about $78.1\%$ boron per mass. However, there is a class of compounds called boranes which also only consist of boron and hydrogen. From this class pentaborane(9), $\ce{B5H9}$, with about $85.7\%$ boron by mass would fit the exercise.


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