Problem 7 - Introductory Chemistry Atoms First

Question

Draw a dot diagram for hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}\), sometimes used as a rocket fuel.

Step-by-Step Solution

Answer

The dot diagram for hydrazine is drawn by first counting the total number of valence electrons, which is 14. The atoms are then connected using single bonds, and any remaining electrons are placed as lone pairs to satisfy the octet rule for the central nitrogen atoms. The final dot diagram for hydrazine is: H H | | N=N | | H H Both nitrogen atoms have 8 electrons surrounding them, and all hydrogen atoms have 2 electrons, adhering to the octet and duet rules respectively.

Step 1: Count the valence electrons

To draw the dot diagram for hydrazine (N₂H₄), first, we need to count the total number of valence electrons in the molecule. Nitrogen has 5 valence electrons and hydrogen has 1 valence electron. Since there are 2 nitrogen atoms and 4 hydrogen atoms in hydrazine, the total number of valence electrons is: \(2 \times 5 + 4 \times 1 = 10 + 4 = 14\)

Step 2: Connect the atoms

Now, we need to connect the atoms in the molecule using single bonds. Place one nitrogen atom in the center and connect the 4 hydrogen atoms and the other nitrogen atom around it. N-H | N-H This uses up 10 valence electrons (2 electrons per single bond).

Step 3: Add lone pairs

Now that the atoms are connected, we must satisfy the octet rule for each of the nitrogen atoms. We currently have 4 electrons left (14 - 10 = 4). Since hydrogen atoms can only have a maximum of 2 electrons, we will only be placing the remaining 4 electrons on the nitrogen atoms as lone pairs. Place two lone pairs on each nitrogen atom. H H | | N=N | | H H Now all 14 valence electrons are used.

Step 4: Check the octet rule

Now that all the valence electrons have been placed, we should check the octet rule. For both nitrogen atoms, there are 8 electrons surrounding them: - 4 electrons from σ bonds (1 single bond with the other nitrogen and 2 single bonds with hydrogen atoms) - 4 electrons in the two lone pairs. All other atoms (the hydrogen atoms) obey the duet rule and are surrounded by 2 electrons (coming from the N-H σ bonds). Therefore, the dot diagram for hydrazine is complete, and the molecule adheres to the octet and duet rules.

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom that are involved in chemical bonding. They are crucial because their arrangement dictates how an atom will interact or bond with other atoms. For hydrazine (\(\mathrm{N}_{2}\mathrm{H}_{4}\)), the number of valence electrons is calculated as follows:

• Nitrogen (N) has 5 valence electrons.
• Hydrogen (H) has 1 valence electron.

The total number of valence electrons for hydrazine is computed by multiplying the number of each atom by their respective valence electrons. Thus:\[2 \times 5 + 4 \times 1 = 14\]In the resulting structure, these valence electrons are strategically distributed to form bonds and lone pairs, ensuring that each atom attains a stable electronic configuration.

Octet Rule

The octet rule is a guiding principle in chemistry that suggests atoms strive to have eight electrons in their valence shell, much like the electron configuration of noble gases. This rule is crucial in understanding how atoms bond in molecules.
For nitrogen atoms in hydrazine, adhering to the octet rule means arranging the electrons to ensure each nitrogen has 8 electrons around it. This can include both bonding electrons in single or double bonds, as well as non-bonding or lone pairs.
In hydrazine:

• Each nitrogen is bonded to one other nitrogen and two hydrogen atoms, contributing to 6 bonding electrons.
• Each nitrogen also has two electrons as lone pairs, bringing their total to 8 electrons.

By fulfilling the octet rule, nitrogen atoms prioritize stability in the molecule, while hydrogen atoms follow the duet rule, attaining stability with 2 electrons, mirroring helium’s configuration.

Molecular Structure

Molecular structure refers to the three-dimensional arrangement of atoms within a molecule. It is crucial as it determines the molecule's properties, reactivity, and bonding behavior. Hydrazine's molecular structure involves arranging the atoms according to their expected geometries and chemical bonds.
The process starts with placing nitrogen atoms at the center (due to their higher valence) and connecting them with hydrogen atoms using single bonds. The idea is to achieve arrangements where the octet rule and other bonding rules are fulfilled.

• The nitrogen atoms form a central chain with the hydrogen atoms branching off.
• Lone pairs are strategically placed on the nitrogen atoms to satisfy their octet requirement while influencing the molecule's shape and reactivity.

Understanding the molecular structure is vital when predicting how hydrazine will interact with other substances, such as oxidizers in rocket fuel applications.

Chemical Bonding

Chemical bonding refers to the attractive forces that hold atoms together in a molecule. These can include covalent, ionic, and metallic bonds, among others. In hydrazine, covalent bonds are formed as atoms share valence electrons to achieve stability.
This molecule specifically utilizes single covalent bonds where:

• Each hydrogen atom shares its one electron with one of the nitrogen atom's electrons, forming \(\sigma\) bonds.
• The nitrogen atoms share electrons to form a single bond with each other, contributing to the molecule's stability and adherence to the octet rule.

Chemical bonding ensures that the essential criteria of the octet and duet rules are met, thereby allowing hydrazine to remain stable and effective as a rocket fuel. These bonds also influence its physical and chemical properties, making it a valuable compound in the aerospace industry.