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

Question

Mateo Aguilar · Accepted Answer

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

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.

Luna Chen · Answer

undefined The empirical formula of the hydrogen atom is CH3.