Which pair shares the same empirical formula?
A. [tex]$C _2 H _4$[/tex] and [tex]$C _6 H _6$[/tex]
B. [tex]$CH _2$[/tex] and [tex]$CH _4$[/tex]
C. [tex]$CH _3$[/tex] and [tex]$C _2 H _6$[/tex]
D. CH and [tex]$C _2 H _4$[/tex]
Answer (2)
Find the greatest common divisor (GCD) for the subscripts in each chemical formula.
Divide the subscripts by their GCD to obtain the empirical formula.
Compare the empirical formulas of each pair.
Identify the pair with matching empirical formulas: C H 3 and C 2 H 6 .
Explanation
Understanding the Problem We are given four pairs of chemical formulas and need to determine which pair shares the same empirical formula. The empirical formula represents the simplest whole-number ratio of atoms in a compound.
Solution Strategy For each pair of chemical formulas, we need to determine the empirical formula by finding the greatest common divisor (GCD) of the subscripts for each element in the compound.
Analyzing Pair 1 Let's analyze each pair:
Pair 1: C 2 H 4 and C 6 H 6
For C 2 H 4 , the GCD of 2 and 4 is 2. Dividing both subscripts by 2, the empirical formula is C H 2 .
For C 6 H 6 , the GCD of 6 and 6 is 6. Dividing both subscripts by 6, the empirical formula is C H .
Analyzing Pair 2 Pair 2: C H 2 and C H 4
The empirical formula for C H 2 is C H 2 because the subscripts are already in the simplest ratio.
The empirical formula for C H 4 is C H 4 because the subscripts are already in the simplest ratio.
Analyzing Pair 3 Pair 3: C H 3 and C 2 H 6
The empirical formula for C H 3 is C H 3 because the subscripts are already in the simplest ratio.
For C 2 H 6 , the GCD of 2 and 6 is 2. Dividing both subscripts by 2, the empirical formula is C H 3 .
Analyzing Pair 4 Pair 4: C H and C 2 H 4
The empirical formula for C H is C H because the subscripts are already in the simplest ratio.
For C 2 H 4 , the GCD of 2 and 4 is 2. Dividing both subscripts by 2, the empirical formula is C H 2 .
Finding the Matching Pair Comparing the empirical formulas for each pair, we find that Pair 3: C H 3 and C 2 H 6 both have the same empirical formula of C H 3 .
Final Answer Therefore, the pair that shares the same empirical formula is C H 3 and C 2 H 6 .
Examples
Understanding empirical formulas is crucial in various real-life applications, such as determining the composition of unknown substances in a laboratory setting. For instance, if you analyze a sample and find it contains carbon and hydrogen in a 1:3 ratio, you know its empirical formula is C H 3 . This information can help you identify the substance or understand its properties. Empirical formulas are also used in combustion analysis to determine the elemental composition of organic compounds, which is vital in fields like environmental science and materials science.
The pair that shares the same empirical formula is C H 3 and C 2 H 6 , both yielding C H 3 . Thus, the correct option is C. This is determined by analyzing the GCD of the subscripts in each formula to find the simplest ratio of elements.
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