Which of the following is the empirical formula for $C _4 H _8$?
A. $CH _4$
B. $CH _2$
C. $C _2 H _2$
D. $C _6 H _6$
Answer (2)
Find the greatest common divisor (GCD) of the subscripts in the molecular formula C 4 H 8 .
Divide each subscript by the GCD.
Simplify the ratio to obtain the empirical formula.
The empirical formula for C 4 H 8 is C H 2 .
Explanation
Understanding the Problem We are given the molecular formula C 4 H 8 and asked to find the empirical formula. The empirical formula represents the simplest whole-number ratio of atoms in a compound.
Finding the GCD To find the empirical formula, we need to find the greatest common divisor (GCD) of the subscripts in the molecular formula C 4 H 8 . The subscripts are 4 and 8.
Calculating the GCD The greatest common divisor (GCD) of 4 and 8 is 4.
Determining the Empirical Formula Now, we divide each subscript by the GCD to obtain the empirical formula. Dividing the subscripts 4 and 8 by 4, we get:
Carbon: 4/4 = 1 Hydrogen: 8/4 = 2
So, the empirical formula is C H 2 .
Selecting the Correct Option Comparing our result with the given options: A. C H 4 B. C H 2 C. C 2 H 2 D. C 6 H 6
The correct answer is B. C H 2 .
Examples
In chemistry, understanding empirical formulas is crucial for determining the simplest ratio of elements in a compound. For instance, if you analyze a sample and find it contains carbon and hydrogen in a 1:2 ratio, the empirical formula C H 2 helps you quickly understand the basic building block of that compound. This knowledge is essential in various applications, such as identifying unknown substances, designing new materials, and understanding chemical reactions. Knowing the empirical formula allows chemists to deduce the molecular formula, which represents the actual number of atoms in a molecule, and further explore the compound's properties and behavior.
The empirical formula for C 4 H 8 is C H 2 because it represents the simplest whole-number ratio of carbon to hydrogen after dividing the subscripts by their greatest common divisor. The correct answer from the options provided is B. C H 2 .
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