Every time a problem provides you with a compound's molar mass, you can use a little trick to help you determine the compound's molecular mass faster.
More specifically, instead of determining the empirical formula first, then using the molar mass to get the molecular formula, you can skip the empirical formula altogether.
As you know, a compound's molar mass tells you what the mass of one mole of that substance is. In this case, one mole of your compound has a mass of 142.00 g.
This means that if you pick a sample of 142.00 g of this compound, you can use its percent composition to get the exact number of moles of each element you get per mole of compound.
So, you know that this compound's percent composition is as follows
carbon→50.7 %
hydrogen→4.2%
oxygen→45.1 %
This means that it contains
142.00 g compound×
100 g compound
50.7 g C
=71.994 g C
142.00 g compound×
100 g compound
4.2 g H
=5.964 g H
142.00 g compound×
100 g compound
45.1 g O
=64.042 g O
Now, all you have to do is use the molar masses of these three elements to determine how many moles of each element you get in one mole of your compound.
For C: 71.994 g×
12.011 g
1 mole C
=5.994≈6
For H: 5.964 g×
1.00794 g
1 mole H
=5.92≈6
For O: 64.042 g×
15.994 g
1 mole O
=4.003≈4
Therefore, the molecular formula of the compound will be C
6H 6 O 4
.
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