Problem 45 - Chemistry The Central Science

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

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 1: 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.

Step 2: 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.

Step 3: 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.

Key Concepts

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.