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Why is it easier to imagine the sample mass as 100 grams when calculating the empirical formula? Also, I just want to confirm that it will only work if we calculated the mass percentage already? And this will work as long as we calculate the mass percentages from the original mass given in the problem?
It's easier to use a 100g sample because we automatically translate the percentages into a mass in grams; there isn't a need to make a calculation. For example: an element X has a 17.8% mass composition. If you give me a 100g sample, I will immediately be able to tell that 17.8% of that sample is 17.8g. If I chose to do this with a 54g sample, I'd be putting myself through the extra trouble of calculating that. And yes, you need to have calculated the mass percentage before proceeding to the 100g step. Supposing that the original mass given is a pure sample of that substance, it will work.
Using 100 grams makes it easier to convert from percentages to grams. For example, if the percentage is 48% then you can convert it to 48 grams since they are both out of 100. This helps you avoid extra steps and extra work to convert the percentages to masses. Hope this helps. :)
When finding the percentage mass, the percentage is out of 100%. This is why pretending to have a sample of 100 grams makes calculations easier as you can easily change a percentage (63%) to be 63 grams due to the new 100 gram sample idea.
We assume 100g of a compound when we are given the mass percent composition but not the actual mass of the compound. It is easy to use 100g because we can convert the percent to grams multiplying by 100. For example if a compound is 35% C, and we assumed the compound is 100g, then we'd have 35g of C. Which then we can use to convert to moles and divide by the lowest moles etc to find the empirical formula. However, if we were provided the total mass of the compound. We don't need to assume 100g. We can just multiply the percent composition by the total mass.
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