Problem 106 - Chemistry: The Central Science

Question

Place the following molecules and ions in order from smallest to largest bond order: \(\mathrm{H}_{2}^{+}, \mathrm{B}_{2}, \mathrm{~N}_{2}^{+}, \mathrm{F}_{2}^{+}\), and \(\mathrm{Ne}_{2}\).

Step-by-Step Solution

Answer

The bond orders of the given molecules and ions are: \(\mathrm{H}_{2}^{+} (0.5) \lt \mathrm{Ne}_{2} (2) \lt \mathrm{B}_{2} (3) \lt \mathrm{F}_{2}^{+} (3.5) \lt \mathrm{N}_{2}^{+} (3.5)\). Therefore, the order from smallest to largest bond orders is: \(\mathrm{H}_{2}^{+}, \mathrm{Ne}_{2}, \mathrm{B}_{2}, \mathrm{F}_{2}^{+},\) and \(\mathrm{N}_{2}^{+}\).

Step 1: Determine the number of electrons in each species

First, we need to determine the total number of electrons in each species. To do this, we will count the number of valence electrons for each atom in the molecule or ion and add or subtract the appropriate number of electrons for any charge on the ion. 1. \(\mathrm{H}_{2}^{+}\): Hydrogen has 1 valence electron, and there are two hydrogen atoms in the molecule. Since there is a +1 charge on the molecule, we will subtract one electron. Total electrons: 1 + 1 - 1 = 1 2. \(\mathrm{B}_{2}\): Boron has 3 valence electrons, and there are two boron atoms in the molecule. Total electrons: 3 + 3 = 6 3. \(\mathrm{N}_{2}^{+}\): Nitrogen has 5 valence electrons, and there are two nitrogen atoms in the molecule. Since there is a +1 charge on the molecule, we will subtract one electron. Total electrons: 5 + 5 - 1 = 9 4. \(\mathrm{F}_{2}^{+}\): Fluorine has 7 valence electrons, and there are two fluorine atoms in the molecule. Since there is a +1 charge on the molecule, we will subtract one electron. Total electrons: 7 + 7 -1 = 13 5. \(\mathrm{Ne}_{2}\): Neon has 8 valence electrons, and there are two neon atoms in the molecule. Total electrons: 8 + 8 = 16

Step 2: Calculate the bond order for each species

Now we will use the molecular orbital diagram and the provided formula to calculate the bond order of each species. 1. \(\mathrm{H}_{2}^{+}\): There is only one electron in bonding orbital, and no electrons in anti-bonding orbitals. Bond order = \(\frac{1}{2}(1 - 0) = 0.5\) 2. \(\mathrm{B}_{2}\): For 6 electrons, there are 6 bonding electrons and 0 anti-bonding electrons. Bond order = \(\frac{1}{2}(6 - 0) = 3\) 3. \(\mathrm{N}_{2}^{+}\): For 9 electrons, there are 8 bonding electrons and 1 anti-bonding electron. Bond order = \(\frac{1}{2}(8 - 1) = 3.5\) 4. \(\mathrm{F}_{2}^{+}\): For 13 electrons, there are 10 bonding electrons and 3 anti-bonding electrons. Bond order = \(\frac{1}{2}(10 - 3) = 3.5\) 5. \(\mathrm{Ne}_{2}\): For 16 electrons, there are 10 bonding electrons and 6 anti-bonding electrons. Bond order = \(\frac{1}{2}(10 - 6) = 2\)

Step 3: Arrange the species in order of bond order

Now that we have found the bond order of each species, we can arrange them in ascending order of bond order: \(\mathrm{H}_{2}^{+} \lt \mathrm{Ne}_{2} \lt \mathrm{B}_{2} \lt \mathrm{F}_{2}^{+} \lt \mathrm{N}_{2}^{+}\)

Key Concepts

Molecular Orbitals

Molecular orbitals are formed when atomic orbitals from different atoms combine during the formation of a molecule. They help us understand chemical bonding by depicting the regions in a molecule where electrons are likely to be found. Unlike atomic orbitals, which belong to individual atoms, molecular orbitals extend over the entire molecule. This means that molecular orbitals can accommodate electrons from different atoms, giving us insight into the molecule's electronic structure and features.

There are two primary types of molecular orbitals: bonding orbitals and antibonding orbitals. Bonding orbitals are lower in energy than the original atomic orbitals, leading to more stability when they are occupied by electrons. Antibonding orbitals are higher in energy and can destabilize a molecule if they are occupied. The arrangement and energy levels of these orbitals can be depicted using molecular orbital diagrams, which are pivotal for calculating bond order.

Valence Electrons

Valence electrons are the outermost electrons of an atom and are involved in chemical reactions and bonding. They determine an atom's ability to bond with other atoms. The behavior and number of valence electrons dictate the chemical properties of elements and are crucial for understanding how molecules form.

The valence electrons can be easily identified from the group number of an element in the periodic table. For instance, all alkali metals have one valence electron, while the noble gases (except Helium) have eight. This information is vital when calculating the total number of electrons in a molecule, as seen in the original exercise. Understanding valence electrons is fundamental to predicting bond formation and the resulting molecular structure.

Chemical Bonds

Chemical bonds are the attractive forces that hold atoms together in molecules. They are essential in creating the stable structures that define substances. There are several types of chemical bonds, such as covalent, ionic, and metallic bonds, but within this context, we focus on covalent bonding.

In covalent bonds, atoms share pairs of valence electrons to achieve a more stable electron configuration. The shared electrons allow each atom to mimic a full outer shell of electrons, often resembling the nearest noble gas configuration. The strength and characteristics of these bonds can be influenced by factors such as overlap of atomic orbitals, which directly tie into molecular orbital theory. Bond order, which is derived from molecular orbitals, gives a quantitative measure of a bond's strength: a higher bond order often indicates a stronger bond.

Bonding and Antibonding Electrons

In molecular orbital theory, bonding and antibonding electrons add detail to how electrons are distributed in a molecule. Bonding electrons are found in molecular orbitals that stabilize the molecule, as they reside within regions of increased electron density that hold atoms together. These electrons fill the bonding molecular orbitals, leading to a stronger bond.

Conversely, antibonding electrons are present in higher-energy molecular orbitals. These electrons can weaken or destabilize a molecule because the presence of electrons in antibonding orbitals reduces the overall electron density between bonding nuclei. This concept is crucial for calculating bond order. The formula for bond order is: \[ \text{Bond Order} = \frac{1}{2}(\text{number of bonding electrons} - \text{number of antibonding electrons}) \]. This relationship underscores the significance of molecular orbitals and plays a key role in explaining the variations in molecular stability and molecular bond strength.