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Chapter 18: Problem 18

Calculate \(\Delta G^{\circ}\) for the following reactions at \(25^{\circ} \mathrm{C}\) : (a) \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) See Appendix 2 for thermodynamic data.

Short Answer

Expert verified
\(\Delta G^{\circ}\) for the first reaction is -1139.2 kJ, for the second reaction is -140 kJ, and for the third reaction is -2712.2 kJ.

Step by step solution

01

Consider the first reaction

The given reaction is: \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\). According to the table in Appendix 2, the standard free energy of formation, \(\Delta G^{\circ}\), for \(\mathrm{MgO}(s)\) is -569.6 kJ. So, \(\Delta G^{\circ}\) for this reaction would be \(2 * (-569.6 kJ) - [2 * 0 + 0] = -1139.2 kJ\).
02

Consider the second reaction

The given reaction is: \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\). From Appendix 2, you get that \(\Delta G^{\circ}\) of \(\mathrm{SO}_{2}(g)\) and \(\mathrm{SO}_{3}(g)\) are -300.4 kJ and -370.4 kJ respectively. The \(\Delta G^{\circ}\) for this reaction would be \(2 * (-370.4 kJ) - [2 * (-300.4 kJ) + 0] = -140 kJ\).
03

Consider the third reaction

The given reaction is: \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\). From Appendix 2, you can find the \(\Delta G^{\circ}\) of \(\mathrm{C}_{2} \mathrm{H}_{6}(g)\), \(\mathrm{CO}_{2}(g)\), \(\mathrm{H}_{2} \mathrm{O}(l)\), which are -32.8 kJ, -394.4 kJ, and -237.1 kJ respectively. So, the calculation yields: \(4 * (-394.4 kJ) + 6 * (-237.1 kJ) - [2 * (-32.8 kJ) + 7 * 0] = -2712.2 kJ\).

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Most popular questions from this chapter

In the Mond process for the purification of nickel, carbon monoxide is reacted with heated nickel to produce \(\mathrm{Ni}(\mathrm{CO})_{4},\) which is a gas and can therefore be separated from solid impurities: $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ Given that the standard free energies of formation of \(\mathrm{CO}(g)\) and \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) are \(-137.3 \mathrm{~kJ} / \mathrm{mol}\) and \(-587.4 \mathrm{~kJ} / \mathrm{mol}\), respectively, calculate the equilibrium constant of the reaction at \(80^{\circ} \mathrm{C}\). Assume that \(\Delta G_{f}^{\circ}\) is temperature independent.

Derive the following equation $$ \Delta G=R T \ln (Q / K) $$ where \(Q\) is the reaction quotient and describe how you would use it to predict the spontaneity of a reaction.

(a) Over the years there have been numerous claims about "perpetual motion machines," machines that will produce useful work with no input of energy. Explain why the first law of thermodynamics prohibits the possibility of such a machine existing. (b) Another kind of machine, sometimes called a “perpetual motion of the second kind," operates as follows. Suppose an ocean liner sails by scooping up water from the ocean and then extracting heat from the water, converting the heat to electric power to run the ship, and dumping the water back into the ocean. This process does not violate the first law of thermodynamics, for no energy is created-energy from the ocean is just converted to electrical energy. Show that the second law of thermodynamics prohibits the existence of such a machine.

Give a detailed example of each of the following, with an explanation: (a) a thermodynamically spontaneous process; (b) a process that would violate the first law of thermodynamics; (c) a process that would violate the second law of thermodynamics; (d) an irreversible process; (e) an equilibrium process.

Without consulting Appendix \(2,\) predict whether the entropy change is positive or negative for each of the following reactions. Give reasons for your predictions. (a) \(2 \mathrm{KClO}_{4}(s) \longrightarrow 2 \mathrm{KClO}_{3}(s)+\mathrm{O}_{2}(g)\) (b) \(\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)\) (d) \(\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{~N}(g)\)
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