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Chapter 2: Problem 45

The structural formulas of the compounds \(n\) -butane and isobutane are shown below.(a) Determine the molecular formula of each.(b) Determine the empirical formula of each. (c) Which formulas - empirical, molecular, or structural- allow you determine these are different compounds?

Short Answer

Expert verified
The molecular formula for both n-butane and isobutane is \(C_4H_{10}\), and their empirical formula is \(C_2H_5\). However, the structural formulas are different: \(CH_3CH_2CH_2CH_3\) for n-butane and \((CH_3)_3CH\) for isobutane, revealing that they are different compounds.

Step by step solution

01

Determine the molecular formula of each

Here, we need to count the number of carbon (C) and hydrogen (H) atoms in the structural formulas of n-butane and isobutane. For n-butane: The structural formula is CH3CH2CH2CH3, so there are 4 carbon atoms and 10 hydrogen atoms. Therefore, the molecular formula for n-butane is C4H10. For isobutane: The structural formula is (CH3)3CH, so there are again 4 carbon atoms and 10 hydrogen atoms. Thus, the molecular formula for isobutane is also C4H10.
02

Determine the empirical formula of each

The empirical formula is the simplest whole number ratio of elements in a compound. For both n-butane and isobutane, the molecular formula is C4H10. The empirical formula can be found by dividing by their greatest common factors. In this case, the greatest common factor is 2 (both numbers can be divided by 2). When we divide C4H10 by the greatest common factor: C4 ÷ 2 = C2 H10 ÷ 2 = H5 So, the empirical formula for both n-butane and isobutane is C2H5.
03

Identify which formula shows the compounds are different

It's important to notice that molecular and empirical formulas are the same for both n-butane and isobutane (C4H10 and C2H5, respectively). However, their structural formulas are different: n-butane has a structural formula of CH3CH2CH2CH3. Isobutane has a structural formula of (CH3)3CH. The structural formula for each compound reveals that they are different compounds, as it shows the unique arrangements and bonding patterns of the atoms within each molecule. Therefore, the structural formula allows us to determine that n-butane and isobutane are different compounds.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molecular Formula
The molecular formula of a compound gives the actual number of atoms of each element present in a molecule. It provides a precise count, not just a simple ratio.
The molecular formula is crucial for understanding the exact composition of a compound but does not reveal how the atoms are arranged or bonded together.
For example, both n-butane and isobutane have the molecular formula
  • C4H10.
This signifies each compound contains
  • 4 carbon atoms
  • 10 hydrogen atoms
Thus, their molecular formulas are identical, despite the two compounds having different structures.
Empirical Formula
The empirical formula is the simplest representation of the relative number of each type of atom in a compound. It is the lowest whole-number ratio of atoms.
To find the empirical formula, divide the subscripts in the molecular formula by their greatest common factor.
For both n-butane and isobutane, you start with the molecular formula
  • C4H10.
The greatest common factor in this case is 2:
  • C4 divided by 2 = C2
  • H10 divided by 2 = H5.
Thus, the empirical formula for both is
  • C2H5.
Keep in mind, while the empirical formula provides an insight into the ratio of atoms, it does not specify the actual arrangement or number of atoms.
Structural Formula
The structural formula offers a more informative representation of a compound. It shows the specific arrangement of atoms and bonds within the molecule, highlighting the three-dimensional structure.
This is especially useful in identifying isomers, compounds with the same molecular formula but different arrangements.
In the case of n-butane and isobutane:
  • n-butane: Represented as CH3CH2CH2CH3, showing a straight-chain structure.
  • isobutane: Has the formula (CH3)3CH, indicating a branched structure.
Thus, without the structural formula, one cannot discern that these are different compounds, even though they share both the molecular and empirical formulas (C4H10 and C2H5).
Hence, it is the structural formula that truly distinguishes isomers by illustrating how atoms are uniquely arranged and connected.

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Most popular questions from this chapter

Mass spectrometry is more often applied to molecules than to atoms. We will see in Chapter 3 that the molecular weight of a molecule is the sum of the atomic weights of the atoms in the molecule. The mass spectrum of \(\mathrm{H}_{2}\) is taken under conditions that prevent decomposition into \(\mathrm{H}\) atoms.The two naturally occurring isotopes of hydrogen are \(^{1} \mathrm{H}\) (atomic mass \(=1.00783\) amu; abundance 99.9885\(\% )\) and 2H (atomic mass \(=2.01410\) amu; abundance 0.0115\(\% ) .\) (a) How many peaks will the mass spectrum have? (b) Give the relative atomic masses of each of these peaks. (c) Which peak will be the largest, and which the smallest?

Many familiar substances have common, unsystematic names. For each of the following, give the correct systematic name: \((\mathbf{a})\)(b) soda ash, saltpeter, \((\mathbf{c})\)soda ash, \(\mathrm{Na}_{2} \mathrm{CO}_{3}$$(\mathbf{d})\)muriatic acid, HCl;\((\mathbf{e})\)Epsom salts, \(\mathrm{Mg} \mathrm{SO}_{4}$$(\mathbf{f})\)milk of magnesia \(\mathrm{Mg}(\mathrm{OH})_{2}\)

What fraction of the \(\alpha\) particles in Rutherford's gold foil experiment are scattered at large angles? Assume the gold foil is two layers thick, as shown in Figure \(2.9,\) and that the approximate diameters of a gold atom and its nucleus are 2.7 A and \(1.0 \times 10^{-4} \hat{\mathrm{A}}\) , respectively. Hint: Calculate the cross sectional area occupied by the nucleus as a fraction of that occupied by the atom. Assume that the gold nuclei in each layer are offset from each other.

(a) What is a functional group? (b) What functional group characterizes an alcohol? (c) Write a structural formula for 1 -pentanol, the alcohol derived from pentane by making a substitution on one of the carbon atoms.

Answer the following questions without referring to Table \(2.1 :\) (a) What are the main subatomic particles that make up the atom? (b) What is the relative charge (in multiples of the electronic charge ) of each of the particles? (c) Which of the particles is the most massive? (d) Which is the least massive?
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