[7.113]When magnesium metal is burned in air (Figure 3.6), two products are produced. One is magnesium oxide, MgO. The other is the product of the reaction of 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 MgO and magnesium nitride after burning is 0.470 g. Water is added to the crucible, further reaction occurs, and the crucible is heated to dryness until the final product is 0.486 g of 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 \(6.3-\mathrm{g}\) 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

01

(a) Formula of Magnesium Nitride

Magnesium has a +2 charge, and the nitride ion has a -3 charge (Table 2.5). To have neutral charges, we need 3 magnesium ions and 2 nitride ions. Therefore, the formula for magnesium nitride is Mg3N2.

02

(b) Balanced Equation of Magnesium Nitride with Water

When magnesium nitride reacts with water, it forms magnesium oxide (MgO) and ammonia gas (NH3). The balanced equation for this reaction is: \( Mg_{3}N_{2} + 6H_{2}O \rightarrow 3MgO + 2NH_{3} \) The driving force for this reaction is the formation of stable magnesium oxide and ammonia gas.

03

(c) Mass Percentage of Magnesium Nitride

First, we determine the moles of MgO produced in the final step: Mass of MgO = 0.486 g Molar mass of MgO = 40.3 g/mol Moles of MgO = Mass of MgO / Molar mass of MgO = 0.486 g / 40.3 g/mol = 0.0121 mol Now, we determine the moles of magnesium nitride in original sample: Moles of magnesium nitride = Moles of MgO formed - Moles of MgO in the original sample = 0.0121 - (0.470 g / 40.3 g/mol) = 0.00236 mol Then, we calculate the mass of the original magnesium nitride: Mass of magnesium nitride = Moles of magnesium nitride * Molar mass of Mg3N2 = 0.00236 mol * 100.9 g/mol = 0.238 g Finally, we determine the mass percentage of magnesium nitride in the original sample: Mass percentage of magnesium nitride = (Mass of magnesium nitride / Mass of the original sample) * 100% = (0.238 g / 0.470 g) * 100% = 50.6 %

04

(d) Balanced Equation of Magnesium and Ammonia

The balanced equation for the reaction of magnesium and ammonia is: \( 3Mg + 2NH_{3} \rightarrow Mg_{3}N_{2} + 3H_{2} \) To determine the limiting reactant, let's find out how many moles of each reactant are present: Moles of Mg = 6.3 g / 24.3 g/mol = 0.259 mol Moles of NH3 = 2.57 g / 17.0 g/mol = 0.151 mol Using the stoichiometry of the balanced equation, it is clear that the limiting reactant is NH3. Now, we can calculate the mass of hydrogen gas formed: Moles of H2 = 3/2 * Moles of NH3 = 0.151 * 3/2 = 0.226 mol Mass of H2 = 0.226 mol * 2.02 g/mol = 0.457 g

05

(e) Standard Enthalpy Change

The standard enthalpy of formation of magnesium nitride is -461.08 kJ/mol. Given the balanced equation: \( 3Mg(s) + 2NH_{3}(g) \rightarrow Mg_{3}N_{2}(s) + 3H_{2}(g) \) For every 1 mol of Mg3N2 formed, 3 mol of magnesium and 2 mol of ammonia are consumed. Therefore, the standard enthalpy change for the reaction between magnesium metal and ammonia gas is: \( ΔH = \frac{-461.08}{3} kJ/mol = -153.69 kJ/mol \)

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