question on chemical calculations, calculating molecular formula

Question

An organic compound contains only C, H and O. If the percentage of carbon by mass is 48.65% and the r.m.m. of the compound is 74, calculate the molecular formula of this compound.

   Please help me find the answer to such a question.

Answer 1

Let's see if we can come up with some equations:

 

Let x be the number of atoms of C in the compound, y the number of H, and z the number of O

 

So 12x + y + 16z = 74.

 

And 12x / 74 = .4865

 

From this equation we get:

12x / 74 = .4865

12x = 36.001

x = 3

 

So there are 3C's.  Good start.

 

Plug that into the first equation:

12*3 + y + 16z = 74

36 + y + 16z = 74

y + 16z = 38

There have to be an integer number of O's, so z can be only 1 or 2.

 

If z = 1, y = 22 and the compound would be C₃H₂₂O

 

If z = 2, y = 6 and the compound would be C₃H₆O₂

 

The first one is impossible, because there wouldn't be enough places to bind 22 atoms of H.

 

So the answer  is C₃H₆O₂