Problem 45 - Chemistry: The Central Science in SI Units, Global Edition

Question

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?

Step-by-Step Solution

Answer

(a) Both n-butane and isobutane have the molecular formula \(C_4H_{10}\). (b) Both compounds also have the same empirical formula, \(C_2H_5\). (c) It is the structural formula that allows us to differentiate between n-butane and isobutane, as they have different arrangements and bonding patterns of atoms.

Step 1: Understanding Molecular, Empirical, and Structural Formulas

Molecular formulas show the actual number of atoms of each element in a molecule. Empirical formulas show the simplest whole number ratio of atoms of each element in a compound. Structural formulas, on the other hand, indicate how the atoms are arranged and bonded to each other in a molecule. Therefore, structural formulas provide more information about the molecule than molecular and empirical formulas.

Step 2: Analyzing the Structural Formulas of n-Butane and Isobutane

Here are the structural formulas for n-butane and isobutane: n-butane: H H H H | | | | C-C-C-C | | | | H H H H isobutane: H H H | | | H-C-C-C-H | | H H We can count the atoms of each element to determine their molecular and empirical formulas.

Step 3: Determining the Molecular Formulas of n-Butane and Isobutane

From the structural formulas, we can easily count the number of carbon and hydrogen atoms in each compound: For n-butane: 4 carbon (C) atoms and 10 hydrogen (H) atoms Therefore, its molecular formula is: \(C_4H_{10}\) For isobutane: 4 carbon (C) atoms and 10 hydrogen (H) atoms Therefore, its molecular formula is: \(C_4H_{10}\) Both compounds have the same molecular formula.

Step 4: Determining the Empirical Formulas of n-Butane and Isobutane

Since both compounds have the same molecular formula, their empirical formulas will also be the same. Their empirical formula will be the simplest whole number ratio of carbon and hydrogen atoms: Dividing both numbers of atoms by their greatest common divisor, which is 2, we obtain 2 and 5. Therefore, the empirical formula of both n-butane and isobutane is: \(C_2H_5\)

Step 5: Identifying the Formula Type That Differentiates the Compounds

Now that we have determined the molecular and empirical formulas for n-butane and isobutane, we can see that these formulas are the same for both compounds, so neither molecular nor empirical formulas can be used to differentiate between them. However, the structural formulas of both compounds are different, indicating that they have different arrangements and bonding patterns of atoms. Thus, the structural formula is the one that allows us to determine that n-butane and isobutane are different compounds. In summary: (a) Molecular formula for n-butane and isobutane: \(C_4H_{10}\) (b) Empirical formula for n-butane and isobutane: \(C_2H_5\) (c) The structural formula allows us to determine that n-butane and isobutane are different compounds.

Key Concepts

Molecular Formula

The molecular formula of a compound reveals the actual number of atoms of each element in a molecule. It provides a direct count of the various atoms present within a single molecule of the substance. For instance, if we take the molecular formula \(C_4H_{10}\), it indicates that the molecule consists of 4 carbon atoms and 10 hydrogen atoms.
Molecular formulas are essential because they give us specific insights into the composition of a chemical substance.
Here are a few points worth remembering regarding molecular formulas:

• They represent the exact number of atoms of each element in a molecule.
• They are useful for calculating molar masses.
• They can be distinct for different substances, but in some cases, different compounds can have the same molecular formula, known as isomers.

Understanding molecular formulas is a stepping stone to delving deeper into a compound's intricacies.

Empirical Formula

The empirical formula is a simplified version of the molecular formula. It shows the smallest whole-number ratio of the atoms of each element in a compound. Even though it provides a basic view of the compound's composition, it's vital for understanding the proportionate makeup of a compound.
For example, let's take the empirical formula \(C_2H_5\), which provides information on the ratio of carbon to hydrogen atoms. Though its molecular formula is \(C_4H_{10}\), the empirical formula simplifies this to its base ratio.
Some important features of empirical formulas include:

• They are derived by dividing the number of each type of atom by their greatest common divisor.
• They do not show the actual number of atoms but tell us about the relative proportions.
• They may represent multiple compounds with the same elemental proportions but different structures.

The empirical formula is like viewing a molecular formula through a magnifying glass that makes the proportions clear.

Structural Formula

The structural formula of a compound offers a detailed insight into the way atoms are arranged and bonded within a molecule. Unlike molecular or empirical formulas, structural formulas are not just about quantity; they showcase the layout and connectivity of atoms.
When you look at the structural formula for compounds such as n-butane and isobutane, you can identify how they have different structures despite having identical molecular formulas.
Consider these points about structural formulas:

• They show the exact arrangement and bonds between atoms in a molecule.
• They help in visualizing different isomers, which have the same molecular formula but differ in arrangement.
• They are crucial in understanding chemical properties and reactivity since structure influences function.

Structural formulas are like blueprints—providing a detailed map of a molecule's architecture and revealing the possible variation between different compounds with the same molecular formula.