Question

Consider the following molecular formulas. How many elements of unsaturation are there in each case? (a) \(\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{NO}\) (b) \(\mathrm{C}_{5} \mathrm{H}_{8} \mathrm{O}_{3} ;\) (c) \(\mathrm{C}_{5} \mathrm{H}_{9} \mathrm{ClO}\).

Short answer

The formula \(C_{5}H_{9}NO\) has 1 element of unsaturation, \(C_{5}H_{8}O_{3}\) has 2 elements of unsaturation, and \(C_{5}H_{9}ClO\) also has 2 elements of unsaturation.

Step-by-step solution

Calculate Unsaturation for Formula (a)

To calculate the elements of unsaturation use the formula \( U = C+1-(H/2) \) for compounds only with Carbon, Hydrogen, and Nitrogen. In this case, \(C = 5\), \(H = 9\) and \(N = 1\). So, \( U = 5+1-(9/2) = 3/2 = 1.5 \). Elements of unsaturation cannot be fractions. This indicates that there is a Nitrogen atom in the molecule which needs to be compensated as Nitrogen can create 3 bonds. So the actual unsaturation which is a whole number is \(1\).

Calculate Unsaturation for Formula (b)

The formula for compounds with Oxygen or without Nitrogen is \( U = C+1-(H/2) \). Here, \(C = 5\), \(H = 8\), and \(O = 3\). This gives, \( U = 5+1-(8/2) = 2 \). So, there are 2 elements of unsaturation in this formula.

Calculate Unsaturation for Formula (c)

The formula for the compounds with Chlorine or halogens is \( U = C+1-(H/2)+X/2 \), where \(X\) denotes halogens. Here, \(C = 5\), \(H = 9\), and \(Cl = 1\). Thus, \( U = 5+1-(9/2)+1/2 = 2.5 \). As explained previously, the element of unsaturation should be a whole number, the fraction indicates there is a halogen present in the molecule. Hence, the real element of unsaturation is \(2\) in this case.

Key concepts

Molecular Formulas

Molecular formulas represent the exact number and type of atoms present in a molecule and are foundational to understanding concepts in organic chemistry. Each atom in the formula contributes to the molecule's properties, including its potential for unsaturation.

For instance, the molecular formula \( \mathrm{C}_{5}\mathrm{H}_{9}\mathrm{NO} \) indicates a compound made of 5 carbon atoms, 9 hydrogen atoms, one nitrogen, and one oxygen atom. These types of formulas are the starting points for further calculations, like determining the number of unsaturation elements, which is crucial for predicting the chemical structure of the compound.

In a molecular formula, carbon (C) and hydrogen (H) atoms are especially indicative of the compound's potential for forming bonds. Other elements such as nitrogen (N), oxygen (O), and halogens like chlorine (Cl) also influence this potential, but they do so in different ways. Understanding the overall composition provided by these formulas is essential for making sense of organic molecules' properties and reactions.

Organic Chemistry

Organic chemistry is the branch of chemistry that studies the structure, properties, and reactions of organic compounds, which are mainly made up of carbon atoms.

The intricacies of organic molecules come from the ability of carbon atoms to form long chains and rings, creating an immense variety of structures. Such versatility allows carbon to make single, double, and even triple bonds with other atoms, fostering the concept of unsaturation. Unsaturation in a molecule reflects the presence of double or triple bonds, or rings, which have a significant impact on how the molecule behaves chemically.

Understanding the degree of unsaturation helps chemists predict how a molecule will react, what its physical characteristics might be, and how it might interact with other molecules. This concept is instrumental in the synthesis and innovation of new organic compounds, including pharmaceuticals, plastics, and other materials that influence our daily lives.

Unsaturation Calculation

The calculation of elements of unsaturation is a method used to deduce possible structures for an organic molecule. It helps in determining the presence of double bonds, triple bonds, or rings within a molecular structure.

The standard formula for calculating unsaturation is \( U = C + 1 - (H/2) \) where \(C\) is the number of carbon atoms and \(H\) is the number of hydrogen atoms. If other elements such as nitrogen, oxygen, or halogens are present, the formula must be adapted accordingly because these atoms interact differently with carbon compared to hydrogen.

For compounds containing nitrogen, its trivalence must be considered, and for those with halogens, the additional fact that halogens are monovalent comes into play. When these elements are present, you might encounter fractional values, as seen in steps 1 and 3 of the provided solution. These fractions are cues that signal the potential structure of the molecule, indicating elements like nitrogen or chlorine. The calculated number of unsaturation elements thus verifies the possibility of double bonds, triple bonds, or rings in the organic molecule's structure, allowing further exploration of the compound's chemical characteristics.