Problem 103 - Chemistry and Chemical Reactivity

Question

The sodium azide required for automobile air bags is made by the reaction of sodium metal with dinitrogen oxide in liquid ammonia: \(3 \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+4 \mathrm{Na}(\mathrm{s})+\mathrm{NH}_{3}(\ell) \longrightarrow\) $$ \mathrm{NaN}_{3}(\mathrm{s})+3 \mathrm{NaOH}(\mathrm{s})+2 \mathrm{N}_{2}(\mathrm{g}) $$ (a) You have \(65.0 \mathrm{g}\) of sodium and a \(35.0-\mathrm{L}\). flask containing \(\mathrm{N}_{2}\) O gas with a pressure of 2.12 atm at \(23^{\circ} \mathrm{C}\) What is the theoretical yield (in grams) of NaNg? (b) Draw a Lewis structure for the azide ion. Include all possible resonance structures. Which resonance structure is most likely? (c) What is the shape of the azide ion?

Step-by-Step Solution

Answer

(a) 46.0 grams of NaN₃. (b) Lewis structures: alternating double bonds resonance. (c) Shape is linear.

Step 1: Calculate Moles of Sodium

Start by calculating the moles of sodium. The molar mass of sodium \( \text{Na} \) is 22.99 g/mol. Use the mass of sodium given to find the moles:\[\text{Moles of Na} = \frac{65.0 \text{ g Na}}{22.99 \text{ g/mol}} \approx 2.83 \text{ moles of Na}\]

Step 2: Determine Moles of N2O

Use the ideal gas law \( PV = nRT \) to calculate the moles of \( \text{N}_2\text{O} \). Rearrange the equation to solve for \( n \) (moles):\[n = \frac{PV}{RT}\]Where \( P \) is 2.12 atm, \( V \) is 35.0 L, \( R \) is 0.0821 L·atm/mol·K, and \( T \) is \( 23°\text{C} + 273.15 = 296.15\text{ K} \).\[n = \frac{2.12 \times 35.0}{0.0821 \times 296.15} \approx 3.03 \text{ moles of N}_2\text{O}\]

Step 3: Identify Limiting Reactant

According to the reaction, 4 moles of \( \text{Na} \) are needed and 3 moles of \( \text{N}_2\text{O} \).Calculate stoichiometric requirements:- Na: \( 2.83/4 = 0.7075 \text{ use factor} \)- N2O: \( 3.03/3 = 1.01 \text{ use factor} \)Na is the limiting reactant because it has the lower use factor.

Step 4: Calculate Theoretical Yield of \( \text{NaN}_3 \)

From the balanced equation, 4 moles of \( \text{Na} \) produce 1 mole of \( \text{NaN}_3 \). Calculate moles of \( \text{NaN}_3 \) from \( \text{Na} \) moles:\[\text{Moles of NaN}_3 = \frac{2.83}{4} = 0.7075 \]Convert moles of \( \text{NaN}_3 \) to grams using its molar mass (65.01 g/mol):\[0.7075 \times 65.01 \approx 46.0 \text{ grams of NaN}_3 \]

Step 5: Draw Lewis Structures for Azide Ion

The azide ion \( \text{N}_3^- \) can have multiple resonance structures. The main structures are:- Structure 1: Central nitrogen with single bonds to each terminal nitrogen, negative charge on one terminal nitrogen.- Structure 2: One double bond with the central nitrogen, alternating positions for double bond and negative charge.A valid alternative is with each terminal nitrogen having a double bond alternatively.

Step 6: Determine Most Likely Resonance Structure

The most stable resonance structure minimizes formal charge dispersion. The structure that delocalizes charge across the ion is often favored. This is usually the one where double bonds alternate, slightly spreading the negative charge across more atoms.

Step 7: Determine Shape of Azide Ion

Using VSEPR theory, the central atom (N) in \( \text{N}_3^- \) has two bonded pairs and zero lone pairs.The structure is linear because it is \( \text{AB}_2 \)-type molecule.Therefore, the shape is linear with bond angles of 180°.

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is based on the balanced chemical equation of the reaction, which indicates the proportion in which substances react and are produced. In the given exercise, the stoichiometry of the reaction between sodium (\(\text{Na}\)), dinitrogen oxide (\(\text{N}_2\text{O}\)), and liquid ammonia (\(\text{NH}_3\)) is key to determining the theoretical yield of sodium azide (\(\text{NaN}_3\)).

To calculate stoichiometry:

• Start by writing the balanced chemical equation.
• Use the molar masses of reactants to convert given weights into moles.
• Apply the mole ratio from the balanced equation to find out how much product can be formed from a given amount of reactant.

This allows chemists to predict how much product will be formed (theoretical yield) in a reaction, provided everything goes to completion. In the exercise, the stoichiometric calculation shows that 4 moles of sodium will produce 1 mole of sodium azide.

Limiting Reactant

In any chemical reaction, it is crucial to determine the limiting reactant as it dictates how much of the product can be formed. The limiting reactant is the substance that runs out first and thus ends the reaction prematurely. In our exercise, sodium (\(\text{Na}\)) was identified as the limiting reactant.

To identify the limiting reactant:

• Calculate the moles of all reactants you have.
• Use the balanced equation to determine the ratio of moles needed between reactants.
• Find out which reactant is present in the smallest ratio; that is your limiting reactant.

By knowing the limiting reactant, you ensure accuracy in calculating theoretical yields as you base your calculations on the reactant that will limit the reaction, thus preventing overestimation.

Lewis Structures

Lewis structures provide a visual representation of the arrangement of atoms in a molecule. They show the bonding between atoms, as well as any lone pairs of electrons. For the azide ion (\(\text{N}_3^-\)), constructing accurate Lewis structures is essential because it helps in understanding its resonant forms and stability.

Key steps to drawing Lewis structures:

• Determine the total number of valence electrons available from the atoms involved.
• Arrange electrons to satisfy the octet rule for each atom, focusing on completing shells with shared (bonding) and lone pairs.
• Consider resonance structures, which are alternative ways to arrange the electrons fulfilling the octet rule.

For the azide ion, important resonance structures include configurations in which nitrogen atoms share double bonds and carry formal charges, allowing for the distribution of negative charge more evenly across the ion. Evaluating these helps to understand which structures are likely to contribute most to the actual electronic structure of the molecule.

VSEPR Theory

VSEPR (Valence Shell Electron Pair Repulsion) theory is used to predict the geometry of individual molecules based on electron-pair interactions. In the case of the azide ion (\(\text{N}_3^-\)), VSEPR theory explains its linear shape.

According to VSEPR theory:

• The shape of a molecule is determined by the number of electron pairs around the central atom, aiming to minimize repulsion by arranging themselves as far apart as possible.
• For the azide ion, the central nitrogen has two regions of electron density (bonds to terminal nitrogen), leading to a linear arrangement to minimize electron repulsion.
• The result is a linear molecule with bond angles of 180°.

Understanding VSEPR theory is critical for predicting and rationalizing the structure of molecules, which directly affects their chemical reactivity and properties.