A sample of a compound is 80% carbon and 20% hydrogen by mass. Its formula mass is 30 amu. What is the molecular formula?

1 Answer
Mar 10, 2017

Answer:

We have #"ethane"#.

Explanation:

As with all these problems, it is usually assumed that we have a #100*g# mass of unknown compound, and we work out the molar quantities:

And thus #"moles of carbon" -=(80*g)/(12.011*g*mol^-1)=6.66*mol#.

And thus #"moles of hydrogen" -=(20*g)/(1.008*g*mol^-1)=19.8*mol#.

We divide the molar quantities thru by the SMALLER molar quantity:

#C:(6.66*mol)/(6.66*mol)=1#

#H:(19.8*mol)/(6.66*mol)=2.97#

And thus the #"empirical formula"# #=# #CH_3#

And we know that the molecular formula is always a multiple of the empirical formula, and thus is terms of mass:

i.e. #"molecular formula"# #=# #nxx"empirical formula"#

But we have a molecular mass of #30*"amu"#

So #30*"amu"# #=# #nxx(12.01+3xx1.01)*"amu"#

Clearly, #n=2#, and the MOLECULAR FORMULA is #C_2H_6#.

This is not a realistic problem, as few analysts would perform combustion on a liquid, and no analyst could perform combustion on a gas.