Ch.5 - Thermochemistry

Problem 113

Chapter 5, Problem 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. (e) The standard enthalpy of formation of solid magnesium nitride is -461.08 kJ>mol. Calculate the standard enthalpy change for the reaction between magnesium metal and ammonia gas.

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Identify the chemical reactions involved: (1) Formation of magnesium nitride from magnesium and nitrogen, and (2) Reaction of magnesium nitride with water to form magnesium oxide and ammonia.

Write the balanced chemical equations for these reactions: (1) \( 3 \text{Mg} + \text{N}_2 \rightarrow \text{Mg}_3\text{N}_2 \) and (2) \( \text{Mg}_3\text{N}_2 + 6\text{H}_2\text{O} \rightarrow 3\text{MgO} + 2\text{NH}_3 \).

Use Hess's Law to find the enthalpy change for the reaction between magnesium metal and ammonia gas. This involves combining the enthalpy changes of the two reactions.

Calculate the enthalpy change for the formation of magnesium nitride using the given standard enthalpy of formation: \( \Delta H_f^\circ (\text{Mg}_3\text{N}_2) = -461.08 \text{ kJ/mol} \).

Determine the overall enthalpy change for the reaction between magnesium metal and ammonia gas by considering the enthalpy changes of the individual reactions and applying Hess's Law.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Enthalpy of Formation

The standard enthalpy of formation (ΔH_f°) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is a crucial concept in thermodynamics, allowing chemists to calculate the energy changes associated with chemical reactions. The values are typically tabulated and can be used to determine the enthalpy change for reactions using Hess's law.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, regardless of the number of steps taken to achieve the reaction. This principle allows for the calculation of enthalpy changes by summing the enthalpy changes of individual steps, making it possible to derive the enthalpy change for complex reactions from simpler ones. It is particularly useful when direct measurement of a reaction's enthalpy change is difficult.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. Understanding stoichiometry is essential for calculating the amounts of substances consumed and produced, as well as for determining the enthalpy changes associated with these reactions. It allows chemists to balance chemical equations and apply the mole concept to predict the outcomes of reactions.

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Textbook Question

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane: 2 CH4(g) → C2H6(g) + H2(g) Calculate the ΔH° for this reaction using the following thermochemical data: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) ΔH° = -890.3 kJ 2 H2(g) + O2(g) → 2 H2O(l) H° = -571.6 kJ 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(l) ΔH° = -3120.8 kJ

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Textbook Question

From the following data for three prospective fuels, calculate which could provide the most energy per unit mass and per unit volume:

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Open Question

The hydrocarbons cyclohexane (C6H12), ΔHf° = -156 kJ/mol, and 1-hexene (C6H12), ΔHf° = -74 kJ/mol, have the same empirical formula. (a) Calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene. (b) Which has greater enthalpy, cyclohexane or 1-hexene?

Open Question

Three hydrocarbons that contain four carbons are listed here, along with their standard enthalpies of formation: Hydrocarbon Formula ΔHfº (kJ/mol) Butane C4H10(g) -125 1-Butene C4H8(g) -1 1-Butyne C4H6(g) 165. (a) For Butane, calculate the molar enthalpy of combustion to CO2(g) and H2O(l). (kJ/mol) (b) For 1-Butene, calculate the molar enthalpy of combustion to CO2(g) and H2O(l). (kJ/mol) (c) For 1-Butyne, calculate the molar enthalpy of combustion to CO2(g) and H2O(l).

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A 201-lb man decides to add to his exercise routine by walking up three flights of stairs (45 ft) 20 times per day. Hefigures that theworkrequired to increasehis potential energy in this way will permit him to eat an extra order of French fries, at 245 Cal, without adding to his weight. Is he correct in this assumption?

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Textbook Question

Sucrose (C12H22O11) is produced by plants as follows: 12 CO2(g) + 11 H2O(l) → C12H22O11 + 12 O2(g) H = 5645 kJ About 4.8 g of sucrose is produced per day per square meter of the earth's surface. The energy for this endothermic reaction is supplied by the sunlight. About 0.1 % of the sunlight that reaches the earth is used to produce sucrose. Calculate the total energy the sun supplies for each square meter of surface area. Give your answer in kilowatts per square meter 1kW/m2 where 1W = 1 J/s2.

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