Question

A hydrogen atom is 84% carbon, by mass. Its relative molecular mass is 100. What is it's empirical formula?

Answer 1

`"A hydrocarbon is 84% carbon by mass..........."`

Explanation:

If that is what the question said, then the empirical formula of the hydrocarbon is `C_7H_16`. How do we know?

`(i)` We assume a mass of `100*g` of hydrocarbon.

`(ii)` We work out its atomic composition on the basis of the atomic percentages:

`"Moles of carbon"` `-=` `(84.0*g)/(12.01*g*mol^-1)=7*mol`

`"Moles of hydrogen"` `-=` `(16.0*g)/(1.00794*g*mol^-1)=16*mol`

How did I know that there were `16*g` of hydrogen based solely on the GIVEN `"% percentage composition of carbon?"`

On this basis, the empirical formula, the simplest whole number representing constituent atoms in a species is `C_7H_16`. Clearly the molecular formula is identical.

It is a fact that the `"molecular formula"` is always a whole number multiple of the `"empirical formula"`.

Thus `"molecular formula"` `=` `nxx"empirical formula"`. But we have been given an estimate of molecular mass. So.............

So `100*"amu"-=(C_7H_16)xxn`

Thus `100*"amu"-=(7xx12.011+16xx1.00794)*"amu"xxn`

We solve for `n` (how), and find `n-=1`.

`"And thus the molecular formula"-=C_7H_16`.

See [here for another example.](https://socratic.org/questions/saccharin-has-the-composition-45-90-c-2-75-h-26-20-o-17-50-s-and-7-65-n-what-is-)