Measurements show that unknown compound X has the following composition: element
mass %
carbon
74.8%
hydrogen
25.1%
Write the empirical chemical formula of X.
X
$
?

the empirical chemical formula of X is CH4

Explanation:Step 1: Imagine you have a sample of compound weighing exactly . Multiply the mass of this sample by the mass percents to find the mass of each element in the sample

Step 2: Divide the mass of each element by the element's molar mass to find the moles of each element in the sample. Remember to round your answers to the correct number of significant digits.  

Step 3: Divide the moles of each element by the the smallest number of moles of any element to find the mole ratio of elements in the sample.  

Step 4: Multiply the mole ratio by the smallest whole number that changes it into a whole number ratio to find the atom ratio of elements in the sample.

Note that the result of each multiplication must equal a whole number only within measurement uncertainty.  

The measurement uncertainty in this calculation comes from the measurement uncertainty of the mass percents given in the question. The mass percents each have significant digits. That means each mass percent has some measurement uncertainty in the third significant digit, and only the first two significant digits can be considered completely reliable.  

In Step 1 you multiplied each mass percent by something with zero uncertainty (the exactly you assumed your sample weighed), in Step 2 you divided by a measurement with more than significant digits (the molar mass of the elements), and in Step 3 you divided by a measurement with the same number of significant digits (the least number of moles of any element in the compound). None of these steps added to the measurement uncertainty of your calculation.  

Therefore, the measurement uncertainty in the final result of all your calculations is determined by the measurement uncertainty in the original mass percents and will be in the third significant digit. That means the result of each of the final multiplication steps must equal a whole number only to within the first two significant digits.  

The whole numbers in the last column of the table are and .  

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