What is the molecular formula of the compound [tex]CH _2[/tex] with molar mass [tex]=168[/tex] [tex]g / mol[/tex]?
A. [tex]C _{10} H _{20}[/tex]
B. [tex]C _{12} H _{24}[/tex]
C. [tex]C _{11} H _{22}[/tex]
D. [tex]C _8 H _{16}[/tex]
Answer (2)
Calculate the molar mass of the empirical formula C H 2 which is approximately 14.026 g/mol.
Divide the molar mass of the compound (168 g/mol) by the molar mass of the empirical formula (14.026 g/mol) to find the multiplier n ≈ 12 .
Multiply the subscripts in the empirical formula C H 2 by n = 12 to obtain the molecular formula C 12 H 24 .
The molecular formula of the compound is C 12 H 24 .
Explanation
Problem Analysis We are given a compound with the empirical formula C H 2 and a molar mass of 168 g/mol. Our goal is to determine the molecular formula of this compound from the given options.
Molar Mass of Empirical Formula First, we need to calculate the molar mass of the empirical formula C H 2 . The molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of hydrogen (H) is approximately 1.008 g/mol. Therefore, the molar mass of C H 2 is:
12.01 + 2 ( 1.008 ) = 12.01 + 2.016 = 14.026 g/mol
Finding the Multiplier Next, we divide the molar mass of the compound (168 g/mol) by the molar mass of the empirical formula (14.026 g/mol) to find the integer n that relates the empirical formula to the molecular formula:
n = 14.026 168 ≈ 11.977 ≈ 12
Determining Molecular Formula Now, we multiply the subscripts in the empirical formula C H 2 by n = 12 to obtain the molecular formula:
C 1 × 12 H 2 × 12 = C 12 H 24
Final Answer Finally, we compare the obtained molecular formula C 12 H 24 with the given options. Option B, C 12 H 24 , matches our result. Therefore, the molecular formula of the compound is C 12 H 24 .
Examples
Understanding molecular formulas is crucial in various fields. For instance, in pharmaceuticals, knowing the precise molecular structure helps in drug design and synthesis. If a chemist discovers a new compound with an empirical formula of C H 2 and determines its molar mass to be 168 g/mol, they can use the method above to find the molecular formula, which is essential for understanding its properties and potential applications. This ensures accurate representation and synthesis of the compound.
The molecular formula of the compound with an empirical formula of C H 2 and a molar mass of 168 g/mol is C 12 H 24 . This is determined by calculating the molar mass of the empirical formula, finding the multiplier, and applying it to the subscripts. Therefore, the correct answer is Option B: C 12 H 24 .
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