A certain sugar has a chemical composition of 40 % carbon, 6.6 % hydrogen, and 53.3 percent oxygen. The molar mass is 180 g/mol. What is the molecular formula?

We assume 100 g of unknown. In such quantity there are:

#((40*g) /(12.01*g*mol^-1))C#; #((6.6*g) /(1.00794*g*mol^-1))H#; and #((53.3*g) /(15.99*g*mol^-1))O#.

Note that I divide thru by the ATOMIC masses of each component.

I gets the ratio: #3.33:6.55:3.33#. Now I divide thru by the lowest quotient to give #C_nH_mO_o# #=# #CH_2O#.

#CH_2O# is the simplest whole number ratio defining constituent atoms in a species; that is, the empirical formula, the formula found by experiment.

Now it is a fact that while the empirical formula may NOT be the same as the molecular formula, the molecular formula is ALWAYS a multiple of the empirical formula.

So, #MF# #=# #(EF)_n#. But we have been given a molecular mass!

And #180*g*mol^-1# #=# #(CH_2O)_n# #=# #(30*g*mol^-1)_n#.

Clearly, #n# #=# #6#. And molecular formula #=# #C_6H_12O_6#, which is probably the stuff you sprinkle on your cornflakes.

Normally, you would not be given the percentage composition of oxygen (because oxygen content can rarely be measured!). A more advanced question would have given percentage compositions of #H# and #C#, and left you to figure out the percentage balance was oxygen content.