Question

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?

Answer 1

`C_6H_12O_6`

Explanation:

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.