Problem 39 - Chemistry and Chemical Reactivity

Question

Dinitrogen monoxide, \(\mathrm{N}_{2} \mathrm{O}\) (commonly called nitrous oxide), is prepared by the careful decomposition of ammonium nitrate and is used as an oxidizing agent in rocket engines as well as a weak general anesthetic (where you may know it as "laughing gas".). However, it is also known to be a powerful greenhouse gas. In a Science magazine article, it was stated that "Human activities may be causing an unprecedented rise in the terrestrial \(\mathrm{N}_{2} \mathrm{O}\) source. Marine \(\mathrm{N}_{2} \mathrm{O}\) production may also rise substantially as result of eutrophication, warming, and ocean acidification." \([\mathrm{L} . \text { A. Codispoti, } \text {Science}\), Vol. \(327, \text { pp. } 1339-1340,2010 .]\) (a) Draw a Lewis electron dot structure for \(\mathrm{N}_{2} \mathrm{O}\) and specify the formal charge on each atom and the molecular geometry. (b) The atom connections are \(\mathrm{N}-\mathrm{N}-\mathrm{O} .\) Why is the connection \(\mathrm{N}-\mathrm{O}-\mathrm{N}\) not likely? (c) The highest \(\mathrm{N}_{2} \mathrm{O}\) concentration observed in the ocean is about 800 nM (nanomolar). At this concentration, what is the mass of \(\mathrm{N}_{2} \mathrm{O}\) per liter?

Step-by-Step Solution

Answer

(a) Lewis structure: N≡N−O with formal charges +1, 0, 0 and linear geometry. (b) N-O-N is unlikely due to instability. (c) Mass of \(\mathrm{N}_2 \mathrm{O}\) is 3.52 µg/L.

Step 1: Draw the Lewis Structure

To draw the Lewis structure of \( \mathrm{N}_2 \mathrm{O} \), start with the skeletal structure \( \mathrm{N} - \mathrm{N} - \mathrm{O} \). Allocate the valence electrons: nitrogen has 5 and oxygen has 6, totaling 16 electrons for two nitrogens and one oxygen. Place one pair of electrons between each bonded pair, giving us 4 electrons used. Distribute the remaining 12 electrons to satisfy the octet rule, forming a triple bond between the nitrogen atoms and a single bond between nitrogen and oxygen, with a lone pair of electrons on the oxygen.

Step 2: Calculate Formal Charges

Calculate the formal charge for each atom: Formal Charge = (Valence Electrons) - (Nonbonding Electrons) - (Bonding Electrons/2). For the \( \mathrm{N} \) connected to \( \mathrm{O} \): 5 - 0 - 8/2 = +1. For the central \( \mathrm{N} \): 5 - 0 - 8/2 = 0. For \( \mathrm{O} \): 6 - 6 - 2/2 = 0. Therefore, the charges are +1 on the \( \mathrm{N} \) nearest \( \mathrm{O} \), 0 on the central \( \mathrm{N} \), and 0 on \( \mathrm{O} \).

Step 3: Determine Molecular Geometry

The molecular geometry around the central nitrogen is linear due to it having two regions of electron density (the triple bond to the first nitrogen and the single bond to oxygen), which aligns in a straight line, resulting in a 180-degree bond angle.

Step 4: Evaluate Connection Preference

The backbone \( \mathrm{N} - \mathrm{N} - \mathrm{O} \) is preferred over \( \mathrm{N} - \mathrm{O} - \mathrm{N} \) because nitrogen can make a triple bond with another nitrogen, satisfying more valence electrons that stabilize the molecule better. \( \mathrm{N} - \mathrm{O} - \mathrm{N} \) would force a less stable configuration where oxygen would form unusual bonding.

Step 5: Concentration to Mass Conversion

The concentration of \( \mathrm{N}_2 \mathrm{O} \) is given as 800 nM. First convert 800 nM to molarity (800 \( \times 10^{-9} \) M). Given the molar mass of \( \mathrm{N}_2 \mathrm{O} \) \( \approx 44.01 \text{ g/mol} \), calculate the mass in grams per liter: \( 800 \times 10^{-9}\, \text{mol/L} \times 44.01\, \text{g/mol} = 3.52 \times 10^{-5} \text{ g/L} \).

Key Concepts

Formal Charge Calculations

Understanding how to calculate formal charges is crucial in determining the most stable Lewis structure for a molecule. Formal charge helps to identify the seemingly best configuration of electrons for atoms in a molecule. To find the formal charge of an atom in a molecule use the formula:

• Formal Charge = (Valence Electrons) - (Nonbonding Electrons) - (Bonding Electrons/2)

For example, in the molecule N i 2 /i O, the atoms are arranged as N-N-O. Here,

• The nitrogen atom connected to the oxygen has a formal charge of +1, calculated as 5 (valence electrons) - 0 (non-bonding electrons) - (8/2) (bonding electrons) = +1.
• The central nitrogen atom has a formal charge of 0 since it's fully bonded with its surrounding atoms using a triple bond to the first N.
• The oxygen atom has a formal charge of 0, calculated by 6 - 6 - (2/2).

Calculating these formal charges ensures that the chosen configuration is the most stable and energetically favorable.

Molecular Geometry

Molecular geometry describes the 3-dimensional shape of a molecule. This is often related to the electron pair repulsion theory which helps predict the arrangement of atoms in a molecule. In N i 2 /i O, the molecular geometry is linear as indicated by its 180-degree bond angle.
The linear shape occurs because there are two regions of electron density forming around the central nitrogen atom:

• A triple bond connecting the first nitrogen to the central nitrogen.
• A single bond connecting the central nitrogen to the oxygen atom.

While drawing molecular structures in two dimensions, geometries like linear, bent, trigonal planar, etc., give insight into how the bonds and atoms will be positioned in space.

Chemical Bonding

Chemical bonding is the process that holds atoms together to form molecules. In N i 2 /i O, nitrogen and oxygen atoms form bonds to produce a stable molecule.
The N-N bonding in this molecule is a triple bond:

• Triple bonds are formed when three pairs of electrons are shared between two atoms. This type of bond is strong and short.

In comparison, the N-O bond in this structure is a single bond, where only one pair of electrons is shared:

• Single bonds allow for the remainder of nitrogen's electrons to form a bond with oxygen, helping to complete the octet for all atoms involved.

Understanding these types of chemical bonding helps comprehend why certain molecular conformations are favored over others.

Greenhouse Gases

Greenhouse gases are compounds that capture heat in Earth's atmosphere, contributing to the greenhouse effect and climate warming. N i 2 /i O, or nitrous oxide, is recognized as one such greenhouse gas.
Human activities significantly increase nitrous oxide levels, resulting from various factors such as agriculture and industrial processes.

• It's used in industries as an oxidizing agent and in medicine as an anesthetic, known as laughing gas.
• Both natural phenomena like eutrophication and man-made events can accelerate its release into the atmosphere, as noted in scientific research.

Addressing N i 2 /i O emissions is important as it has substantial impacts on climate change. Understanding its chemical makeup and atmospheric behavior can aid in the development of strategies to mitigate its environmental impact.