Problem 110 - Chemistry The Central Science

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

The formula of magnesium nitride is \(\mathrm{Mg}_{3}\mathrm{N}_{2}\). The balanced equation for the reaction with water is \(3 \mathrm{Mg}_{3}\mathrm{N}_{2}(s) + 6 \mathrm{H}_{2}\mathrm{O}(l) \to 9 \mathrm{MgO}(s) + 6\mathrm{NH}_{3}(g)\), and its driving force is the formation of stable magnesium oxide and ammonia gas. The mass percentage of magnesium nitride in the mixture obtained after the initial burning is 3.40%. The balanced equation for the reaction with ammonia is \(3\,\mathrm{Mg}(s) \,+\, 2\,\mathrm{NH}_{3}(g) \,\to \,\mathrm{Mg}_{3}\mathrm{N}_{2}(s) \,+\, 3\,\mathrm{H}_{2}(g)\), and the limiting reactant is \(\mathrm{NH}_{3}\) with 0.457 g of hydrogen gas formed. The standard enthalpy change for the reaction between magnesium metal and ammonia gas is -461.08 kJ/mol.

Step 1: Identify the charges of magnesium and nitride ions

Magnesium ion has a charge of +2, and the nitride ion has a charge of -3.

Step 2: Determine the formula

To determine the formula, balance the charges in the compound. We need 2 nitride ions (-3 each) to balance with 3 magnesium ions (+2 each): \[3 \mathrm{Mg}^{2+} + 2 \mathrm{N}^{3-} \to \mathrm{Mg}_{3}\mathrm{N}_{2}\] The formula of magnesium nitride is \(\mathrm{Mg}_{3}\mathrm{N}_{2}\). b) Write a balanced equation for the reaction of magnesium nitride with water and identify the driving force of the reaction:

Step 1: Write the unbalanced equation

Mg3N2 (s) + H2O (l) -> MgO (s) + NH3 (g)

Step 2: Balance the equation

Balance the equation: \[3 \mathrm{Mg}_{3}\mathrm{N}_{2}(s) + 6 \mathrm{H}_{2}\mathrm{O}(l) \to 9 \mathrm{MgO}(s) + 6\mathrm{NH}_{3}(g)\]The driving force for this reaction is the formation of stable magnesium oxide and ammonia gas. c) Calculate the mass percentage of magnesium nitride in the mixture.

Step 1: Calculate the mass of magnesium oxide formed

The final mass of magnesium oxide is 0.486 g, and the initial mass of the mixture after burning is 0.470 g. Thus, the mass of magnesium oxide formed is 0.486 g - 0.470 g = 0.016 g.

Step 2: Calculate the mass of magnesium nitride consumed

The mass of magnesium nitride consumed equals the mass of magnesium oxide formed. So, the mass of Mg3N2 consumed is 0.016 g.

Step 3: Calculate the mass percentage of magnesium nitride in the mixture

Mass percentage of Mg3N2 is: \[\frac{0.016\,\text{g}}{0.470\,\text{g}} \times 100 = 3.40\%\] d) Write a balanced equation for the reaction of magnesium nitride with ammonia, determine the limiting reactant, and find the mass of hydrogen gas formed.

Step 1: Write the balanced equation

\[3\,\mathrm{Mg}(s) \,+\, 2\,\mathrm{NH}_{3}(g) \,\to \,\mathrm{Mg}_{3}\mathrm{N}_{2}(s) \,+\, 3\,\mathrm{H}_{2}(g)\]

Step 2: Determine the limiting reactant

Given masses: Mg = 6.3 g and NH3 = 2.57 g Molar mass of Mg = 24.31 g/mol, Molar mass of NH3 = 17.03 g/mol Moles of Mg = 6.3 g / 24.31 g/mol = 0.259 mol Moles of NH3 = 2.57 g / 17.03 g/mol = 0.151 mol Mole ratio of Mg to NH3 = 3:2, so 0.259 mol Mg * (2/3) = 0.173 mol NH3 required. Since 0.151 mol NH3 is available and 0.173 mol is required, NH3 is the limiting reactant.

Step 3: Calculate mass of hydrogen gas formed

Moles of H2 = 0.151 mol NH3 * (3/2) H2/NH3 = 0.226 mol H2 Molar mass of H2 = 2.02 g/mol Mass of H2 formed = 0.226 * 2.02 = 0.457 g e) Calculate the standard enthalpy change for the reaction between magnesium metal and ammonia gas.

Step 1: Obtain the standard enthalpy change of Mg3N2 formation

Standard enthalpy of formation of Mg3N2: \(\Delta H_{f}^{\circ}\)(Mg3N2) = -461.08 kJ/mol

Step 2: Obtain the standard enthalpy change of the reaction

The balanced equation for the reaction is: \[3\,\mathrm{Mg}(s) \,+\, 2\,\mathrm{NH}_{3}(g) \,\to \,\mathrm{Mg}_{3}\mathrm{N}_{2}(s) \,+\, 3\,\mathrm{H}_{2}(g)\] The standard enthalpy change of the reaction is equal to the standard enthalpy of formation of Mg3N2: \[\Delta H^{\circ} = \Delta H_{f}^{\circ}(\mathrm{Mg}_{3}\mathrm{N}_{2}) = -461.08\text{ kJ/mol}\]

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of bonds. In this exercise, when magnesium is burned, it reacts with oxygen in the air to form magnesium oxide (MgO). Additionally, it reacts with nitrogen to form magnesium nitride (Mg\(_3\)N\(_2\)). Such reactions are examples of combustion and nitride formation, showcasing how elements can combine to create new compounds.

When Magnesium nitride reacts with water, it forms magnesium oxide and ammonia gas. This is another type of chemical reaction, known as a hydrolysis reaction, where a compound reacts with water to form new products. Recognizing these reactions as chemical transformations helps in understanding how different substances interact to form entirely new materials.

Stoichiometry

Stoichiometry is the study of quantitative relationships in chemical reactions. It allows us to determine how much of each reactant is required to form a given product. In any given reaction, such as the formation or decomposition of magnesium nitride, stoichiometry provides a balanced equation that ensures the conservation of mass.

• For the decomposition of magnesium nitride and reaction with water, the balanced equation is: 3 Mg\(_3\)N\(_2\) + 6 H\(_2\)O → 9 MgO + 6 NH\(_3\). This shows the stoichiometric coefficients indicating the relative number of molecules involved.
• The balanced equation allows us to calculate the precise amounts of substances needed or produced in a reaction, ensuring we have exact values that correspond with the law of conservation of mass.

Limiting Reactant

The limiting reactant is the substance that is completely consumed in a chemical reaction, determining the maximum amount of product that can be formed. In reactions with set amounts of multiple reactants, the one that produces the least amount of product controls the output.

In our exercise, when magnesium nitride is formed by reacting magnesium with ammonia, we need to determine which reactant limits the reaction. The calculated moles of magnesium and ammonia showed ammonia as the limiting reactant, meaning it is exhausted first, stopping more product from forming.

• Moles of Mg available = 0.259 mol
• Moles of NH\(_3\) required = 0.173 mol, but only 0.151 mol is present

This understanding is crucial in real-world applications where resource efficiency is important.

Enthalpy Change

Enthalpy change (\( \Delta H \)) refers to the heat absorbed or released during a chemical reaction at constant pressure. A negative \( \Delta H \) suggests an exothermic reaction, indicating that heat is released.

In the case of magnesium reacting with ammonia to form magnesium nitride, the enthalpy change is negative (-461.08 kJ/mol), highlighting the exothermic nature of the reaction. This means that forming magnesium nitride from magnesium and ammonia releases a significant amount of energy as heat into the surroundings.

• A negative standard enthalpy change implies the product is more stable than the reactants.
• Understanding enthalpy helps predict reaction behavior and is crucial for energy management in chemical processes.