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Chapter 5: Problem 43

Consider the following reaction: $$ 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) \quad \Delta H=-1204 \mathrm{~kJ} $$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when \(3.55 \mathrm{~g}\) of \(\mathrm{Mg}(s)\) reacts at constant pressure. (c) How many grams of \(\mathrm{MgO}\) are produced during an enthalpy change of \(-234 \mathrm{~kJ}\) ? (d) How many kilojoules of heat are absorbed when \(40.3 \mathrm{~g}\) of \(\mathrm{MgO}(s)\) is decomposed into \(\mathrm{Mg}(s)\) and \(\mathrm{O}_{2}(g)\) at constant pressure?

Short Answer

Expert verified
(a) The reaction is exothermic since \(\Delta H = -1204 \mathrm{~kJ}\) is negative. (b) The amount of heat transferred when \(3.55 \mathrm{~g}\) of Mg reacts at constant pressure is \(-88.1 \mathrm{~kJ}\). (c) \(15.6 \mathrm{~g}\) of MgO are produced during an enthalpy change of \(-234 \mathrm{~kJ}\). (d) \(602 \mathrm{~kJ}\) of heat are absorbed when \(40.3 \mathrm{~g}\) of MgO is decomposed into Mg and O2 at constant pressure.

Step by step solution

01

(a) Identify Reaction Type:

To determine if the reaction is exothermic or endothermic, we need to look at the value of the enthalpy change during the reaction, which is given as \(\Delta H = -1204 \mathrm{~kJ}\). A negative value of \(\Delta H\) indicates that the reaction releases heat, making it an exothermic reaction.
02

(b) Calculate Heat Transferred:

First, we need to find the molar mass of magnesium, which is found to be 24.305 g/mol by checking a periodic table. Then, we will determine the moles of magnesium that reacted, and use the stoichiometry of the balanced chemical equation to find the heat transferred. 1. Find the moles of Mg that reacted: Moles of Mg = (mass of Mg) / (molar mass of Mg) = (3.55 g) / (24.305 g/mol) = 0.146 mol Mg 2. Use stoichiometry to find the heat released: Moles of heat = 2 moles of Mg -> -1204 kJ Moles of heat = 0.146 moles of Mg -> x kJ x = (0.146 mol Mg) * (-1204 kJ) / (2 mol Mg) = -88.1 kJ So, the amount of heat transferred when 3.55 g of Mg reacts at constant pressure is -88.1 kJ.
03

(c) Calculate Mass of MgO Produced:

In this problem, we are given the enthalpy change and need to find the mass of MgO produced. Using the balanced chemical equation and the molar mass of MgO, we can find the mass of MgO produced. 1. Use stoichiometry to find the moles of MgO produced: Enthalpy change = 2 moles of MgO -> -1204 kJ Enthalpy change = x moles of MgO -> -234 kJ x = ( -234 kJ) * (2 mol MgO) / (-1204 kJ) = 0.388 mol MgO 2. Find the mass of MgO produced: Molar mass of MgO = 40.305 g/mol Mass of MgO = (moles of MgO) * (molar mass of MgO) = (0.388 mol MgO) * (40.305 g/mol) = 15.6 g So, 15.6 g of MgO are produced during an enthalpy change of -234 kJ.
04

(d) Calculate Heat Absorbed:

In this problem, we are given the mass of MgO decomposed and need to find the heat absorbed. Using the balanced chemical equation, we can find the heat absorbed. 1. Find the moles of MgO decomposed: Moles of MgO = (mass of MgO) / (molar mass of MgO) = (40.3 g) / (40.305 g/mol) = 1.00 mol MgO 2. Use stoichiometry to find the heat absorbed: Enthalpy change = 2 moles of MgO -> -1204 kJ Enthalpy change = 1.00 mole of MgO -> x kJ x = (1.00 mol MgO) * (-1204 kJ) / (2 mol MgO) = +602 kJ Note that this value is positive because the reaction is reversed. In this case, the reaction is endothermic when going in the reverse direction. So, 602 kJ of heat are absorbed when 40.3 g of MgO is decomposed into Mg and O2 at constant pressure.

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Most popular questions from this chapter

In the accompanying cylinder diagram a chemical process occurs at constant temperature and pressure. (a) Is the sign of \(w\) indicated by this change positive or negative? (b) If the process is endothermic, does the internal energy of the system within the cylinder increase or decrease during the change and is \(\Delta E\) positive or negative? [Sections \(5.2\) and \(5.3\) ]

The standard enthalpies of formation of gaseous propyne \(\left(\mathrm{C}_{3} \mathrm{H}_{4}\right)\), propylene \(\left(\mathrm{C}_{3} \mathrm{H}_{6}\right)\), and propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) are \(+185.4,+20.4\), and \(-103.8 \mathrm{~kJ} / \mathrm{mol}\), respectively. (a) Calculate the heat evolved per mole on combustion of each substance to yield \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\). (b) Calculate the heat evolved on combustion of \(1 \mathrm{~kg}\) of each substance. (c) Which is the most efficient fuel in terms of heat evolved per unit mass?

The complete combustion of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), to form \(\mathrm{H}_{2} \mathrm{O}(g)\) and \(\mathrm{CO}_{2}(g)\) at constant pressure releases \(1235 \mathrm{~kJ}\) of heat per mole of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). (a) Write a balanced thermochemical equation for this reaction. (b) Draw an enthalpy diagram for the reaction.

Diethyl ether, \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)\), a flammable compound that has long been used as a surgical anesthetic, has the structure $$ \mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{2}-\mathrm{O}-\mathrm{CH}_{2}-\mathrm{CH}_{3} $$ The complete combustion of \(1 \mathrm{~mol}\) of \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}(l)\) to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(I)\) yields \(\Delta H^{\circ}=-2723.7 \mathrm{~kJ}\). (a) Write a balanced equation for the combustion of \(1 \mathrm{~mol}\) of \(\mathrm{C}_{4} \mathrm{H}_{40} \mathrm{O}(l)\). (b) By using the information in this problem and data in Table 5.3, calculate \(\Delta H_{f}^{\circ}\) for diethyl ether.

(a) What is meant by the term system in thermodynamics? (b) What is a closed system? (c) What do we call the part of the universe that is not part of the system?
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