What is the empirical formula of $C _8 H _{16} O _8$?
Answer (2)
Find the greatest common divisor (GCD) of the subscripts: GCD(8, 16, 8) = 8.
Divide each subscript by the GCD: Carbon: 8/8 = 1 , Hydrogen: 16/8 = 2 , Oxygen: 8/8 = 1 .
Write the empirical formula using the new subscripts: C H 2 O .
The empirical formula is C H 2 O .
Explanation
Understanding the Problem We are given the molecular formula C 8 H 16 O 8 and asked to find the empirical formula. The empirical formula represents the simplest whole-number ratio of atoms in a compound. To find it, we need to determine the greatest common divisor (GCD) of the subscripts in the molecular formula and divide each subscript by the GCD.
Finding the GCD The subscripts in the molecular formula C 8 H 16 O 8 are 8, 16, and 8. We need to find the greatest common divisor (GCD) of these numbers.
Calculating the GCD The GCD of 8 and 16 is 8, since 8 divides both 8 and 16. Then we find the GCD of 8 and 8, which is 8. Therefore, the GCD of 8, 16, and 8 is 8.
Determining the Empirical Formula Now, we divide each subscript in the molecular formula by the GCD (which is 8) to obtain the empirical formula:
Carbon: 8/8 = 1 Hydrogen: 16/8 = 2 Oxygen: 8/8 = 1
So, the empirical formula is C 1 H 2 O 1 , which is written as C H 2 O .
Final Answer The empirical formula of C 8 H 16 O 8 is C H 2 O .
Examples
Understanding empirical formulas is crucial in various fields. For instance, in nutrition, knowing the empirical formula of a carbohydrate helps determine its basic structure and how it provides energy. If a carbohydrate has the molecular formula C 6 H 12 O 6 (glucose), its empirical formula is C H 2 O , indicating a 1:2:1 ratio of carbon, hydrogen, and oxygen atoms. This knowledge aids in classifying and understanding the properties of different carbohydrates and their roles in biological processes.
The empirical formula of C 8 H 16 O 8 is C H 2 O , which represents the simplest ratio of its constituent elements. We find this by dividing each subscript by the greatest common divisor, which in this case is 8. The process results in the subscripts 1 for Carbon, 2 for Hydrogen, and 1 for Oxygen.
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