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In homework problem F.1, I counted the number of atoms in the model. I got a molecular formula of C10 H16 O. It asks for the mass % composition. So, for this case do I assume the molecule is 100g to find the mass % of each element this way?
In order to find the mass percentage composition of citral, you would multiply the number of carbon atoms by the molar mass of a carbon atom. Since there are 10 atoms of carbon, you would multiply it by 12.01 (mass of carbon) giving you a total of 120.1 g/mol. You would do the same for hydrogen and oxygen with their respective molar masses and total number of atoms in citral. Once you have the masses of all the elements in citral, you would add them together in order to find the molar mass of citral, which is 152.3 g/mol. To find the mass percentage of carbon in this molecule, you would divide the mass of the carbon atoms by the total mass of citral and multiply the value that you get by 100, giving you the mass percentage of carbon. In this case, you would divide 120.1 g/mol by 152.3 g/mol and multiply it by a 100, giving you a mass percentage composition of carbon of 78.90%. You would follow the same steps for hydrogen and oxygen. These percentages should eventually add up to a 100%.
I am still a bit confused about when to divide the mass percentage by 100g and when to just take the percentage and make it into grams. For example, in the homework problem E.11, we took the percentages like 7.42% from one of the isotopes and divided by 100 to get 0.0742. However, when looking at the homework problem H.25 we did not divide the % by 100g. For example, in H.25, 43.64% just turned into 43.64g. Could someone please clarify/explain how to determine which method to use when turning % to grams?
turning the given % to grams just makes it easier to visualize the distribution of weight among the compound. Once you convert the % to the corresponding grams (in relation to 100g), it is much easier to determine the empirical formula as you are now able to use these theoretical weights and compare it to the known molar masses of the elements fo the compound. This method generally is used when you are given theoretical percentages and asked to determine the empirical formula. However, if you are given percentages and a known total mass of the compound, just apply the percentages to the given mass of the compound and determine the number of moles, empirical formula, and then the molecular formula (if asked by the question).
In this case, it is easier to find the mass % composition based on the mass of the actual sample rather than assuming 100 grams because it takes fewer steps to do so. It is simplest to calculate the molar mass of the sample (152.2 grams) and then divide the molar mass of each individual element within the sample by the total sample mass. In this case, carbon is 10(12.011g/mol) / 152.2g = 0.789 x 100 = 78.9% of the total mass, hydrogen is 16(1.008) / 152.2g = .106 x 100 = 10.6% of the total mass, and oxygen is 16g/mol / 152.2g = .105 x 100 = 10.5% of the total mass. To double-check that my work is correct, I add up 78.9, 10.6, and 10.5 and get 100 as a result. This proves that my work is correct.
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