Problem 113 - Chemistry The Central Science In Si Units

Question

When magnesium metal is burned in air (Figure 3.6), two products are produced. One is magnesium oxide, \(\mathrm{MgO}\). The other is the product of the reaction of \(\mathrm{Mg}\) with molecular nitrogen, magnesium nitride. When water is added to magnesium nitride, it reacts to form magnesium oxide and ammonia gas. (a) Based on the charge of the nitride ion (Table 2.5), predict the formula of magnesium nitride. (b) Write a balanced equation for the reaction of magnesium nitride with water. What is the driving force for this reaction? (c) In an experiment, a piece of magnesium ribbon is burned in air in a crucible. The mass of the mixture of \(\mathrm{MgO}\) and magnesium nitride after burning is \(0.470 \mathrm{~g}\). Water is added to the crucible, further reaction occurs, and the crucible is heated to dryness until the final product is \(0.486 \mathrm{~g}\) of \(\mathrm{MgO}\). What was the mass percentage of magnesium nitride in the mixture obtained after the initial burning? (d) Magnesium nitride can also be formed by reaction of the metal with ammonia at high temperature. Write a balanced equation for this reaction. If a 6.3-g Mg ribbon reacts with \(2.57 \mathrm{~g} \mathrm{NH}_{3}(g)\) and the reaction goes to completion, which component is the limiting reactant? What mass of \(\mathrm{H}_{2}(g)\) is formed in the reaction? (e) The standard enthalpy of formation of solid magnesium nitride is \(-461.08 \mathrm{~kJ} / \mathrm{mol}\). Calculate the standard enthalpy change for the reaction between magnesium metal and ammonia gas.

Step-by-Step Solution

Answer

Magnesium nitride formula: \(\text{Mg}_3\text{N}_2\). Limiting reactant: \(\text{NH}_3\). Mass of \(\text{H}_2\): 0.456 g. Mass percentage of \(\text{Mg}_3\text{N}_2\): use stoichiometry of \(\text{Mg}_3\text{N}_2\) reaction. Enthalpy change: -369.28 kJ/mol.

Step 1: Determine Formula of Magnesium Nitride

The nitride ion has a charge of -3. Magnesium, an alkaline earth metal, has a charge of +2 when it forms ions. Therefore, to balance the charges in magnesium nitride, we need three Mg ions to balance out two nitride ions. The formula for magnesium nitride is \(\text{Mg}_3\text{N}_2\).

Step 2: Balanced Equation for Magnesium Nitride Reaction with Water

When magnesium nitride reacts with water, magnesium oxide and ammonia are formed. Start by writing the formula: \(\text{Mg}_3\text{N}_2 + 6\text{H}_2\text{O} \rightarrow 3\text{MgO} + 2\text{NH}_3\). The driving force is the formation of stable compounds MgO and NH3.

Step 3: Mass Percentage of Magnesium Nitride

Initial mass of mixture = 0.470 g. After reaction with water and forming MgO, the final mass = 0.486 g. Extra mass formed = \(0.486 - 0.470 = 0.016\) g, which corresponds to the ammonia reacting with water. Use the stoichiometry of \(\text{Mg}_3\text{N}_2\) reaction, relating change in mass to calculate mass of \(\text{Mg}_3\text{N}_2\). Percentage mass of \(\text{Mg}_3\text{N}_2 = \frac{\text{mass of } \text{Mg}_3\text{N}_2}{0.470} \times 100\).

Step 4: Balanced Equation for Reaction with Ammonia

Magnesium reacts with ammonia as follows: \(3\text{Mg} + 2\text{NH}_3 \rightarrow \text{Mg}_3\text{N}_2 + 3\text{H}_2\).

Step 5: Determine Limiting Reactant

Calculate moles of Mg (molar mass = 24.305 g/mol) and \(\text{NH}_3\) (molar mass = 17.03 g/mol). \(\frac{6.3}{24.305}\approx 0.259\) moles of Mg and \(\frac{2.57}{17.03}\approx 0.151\) moles of \(\text{NH}_3\). Based on stoichiometry (3 moles Mg for every 2 moles \(\text{NH}_3\)), \(\text{NH}_3\) is the limiting reactant.

Step 6: Mass of Hydrogen Gas Formed

From the balanced equation \(3\text{Mg} + 2\text{NH}_3 \rightarrow \text{Mg}_3\text{N}_2 + 3\text{H}_2\), 0.151 moles of \(\text{NH}_3\) will produce 0.226 moles of \(\text{H}_2\) (3 times 0.151). Mass of \(\text{H}_2\) (molar mass = 2.016 g/mol) = \(0.226 \times 2.016 \approx 0.456\) g.

Step 7: Enthalpy Change for Reaction

The reaction is \(3\text{Mg} + 2\text{NH}_3 \rightarrow \text{Mg}_3\text{N}_2 + 3\text{H}_2\). Use the enthalpy of formation: \(\Delta H = [1 \times (-461.08)] - [2 \times (-45.9)]\). \(\Delta H = -369.28\) kJ/mol.

Key Concepts

Magnesium Nitride

Magnesium nitride is a chemical compound formed by the combination of magnesium and nitrogen. In terms of chemical formula, it is represented as \( \text{Mg}_3\text{N}_2 \). This formula results from the need to balance the charges of magnesium and nitride ions. Magnesium ions carry a +2 charge, while nitride ions have a -3 charge. Therefore, to achieve neutrality, three magnesium ions are required to pair with two nitride ions.

• Magnesium belongs to the alkaline earth metals group and commonly forms ions with a +2 charge.
• Nitrogen atoms gain electrons to form a nitride ion with a -3 charge.
• The resulting magnesium nitride is a white or grayish solid.

Understanding the formation and composition of magnesium nitride is important in predicting the chemical reactions it can undergo.

Balanced Chemical Equations

Balance in chemical equations is crucial to accurately represent a chemical reaction. A balanced equation ensures that the number of each type of atom is the same on both sides, following the Law of Conservation of Mass. Let's consider the reaction of magnesium nitride with water:
In the reaction \( \text{Mg}_3\text{N}_2 + 6\text{H}_2\text{O} \rightarrow 3\text{MgO} + 2\text{NH}_3 \), each side of the equation must display the same number of atoms for each element:

• 3 magnesium (\( \text{Mg} \)) atoms on both sides.
• 2 nitrogen (\( \text{N} \)) atoms on both sides.
• 12 hydrogen (\( \text{H} \)) atoms on each side.
• 6 oxygen (\( \text{O} \)) atoms appearing as part of \( \text{H}_2\text{O} \) and \( \text{MgO} \).

Balanced equations are foundational in calculating the amounts of reactants or products in a reaction.

Limiting Reactants

In chemical reactions, the limiting reactant is the substance that runs out first, effectively ending the reaction. When burning magnesium ribbon in the presence of ammonia, we need to identify which reactant is limiting to determine how much product can form.
For the reaction \( 3\text{Mg} + 2\text{NH}_3 \rightarrow \text{Mg}_3\text{N}_2 + 3\text{H}_2 \):

• Calculate the moles of each reactant. Magnesium's molar mass is approximately 24.305 g/mol, and ammonia's molar mass is about 17.03 g/mol.
• From the problem, 6.3 g of magnesium provides \( \frac{6.3}{24.305} \approx 0.259 \) moles.
• 2.57 g of ammonia provides \( \frac{2.57}{17.03} \approx 0.151 \) moles.
• According to the equation's stoichiometry, 3 moles of \( \text{Mg} \) are needed to fully react with 2 moles of \( \text{NH}_3 \), so \( \text{NH}_3 \) is the limiting reactant.

The limiting reactant determines the maximum amount of product that can be formed, guiding predictions and calculations in practical applications.

Standard Enthalpy Change

The standard enthalpy change of a reaction refers to the heat exchanged with the surroundings at constant pressure and under standard conditions (298 K, 1 atm). It provides insight into the energy dynamics of the reaction, identifying whether it is endothermic or exothermic.
In the reaction \( 3\text{Mg} + 2\text{NH}_3 \rightarrow \text{Mg}_3\text{N}_2 + 3\text{H}_2 \), we utilize the standard enthalpy of formation:

• Given the enthalpy of magnesium nitride \( \text{Mg}_3\text{N}_2 \) formation is \(-461.08 \) kJ/mol.
• The standard enthalpy of formation for ammonia \( \text{NH}_3 \) is approximately \(-45.9 \) kJ/mol.
• The standard enthalpy change for the overall reaction is calculated as: \[ \Delta H = [1 \times (-461.08)] - [2 \times (-45.9)] = -369.28 \text{ kJ/mol}. \]
• This negative value indicates the reaction is exothermic, releasing heat into the surroundings.

Understanding enthalpy change is crucial for comprehending the energy flow in chemical processes.