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Chapter 16: Problem 43

For each of the following pairs of substances, which substance has the greater value of \(S^{\circ} ?\) a. \(\mathrm{C}_{\text {graphite }}(s)\) or \(\mathrm{C}_{\text {diamond }}(s)\) b. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) or \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)\) c. \(\mathrm{CO}_{2}(s)\) or \(\mathrm{CO}_{2}(g)\)

Short Answer

Expert verified
For each pair of substances, the substance with the greater value of \(S^\circ\) is as follows: a. Graphite carbon: \(\mathrm{C}_{\text{graphite}}(s)\) b. Gaseous ethanol: \(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}(g)\) c. Gaseous carbon dioxide: \(\mathrm{CO}_{2}(g)\)

Step by step solution

01

a. Graphite and diamond carbon

Graphite and diamond both have the same chemical formula (C, carbon), but they have different crystalline structures, which influence their entropy. In graphite, carbon atoms are arranged in a layered, planar structure with relatively weak intermolecular forces between those layers, allowing them to slide past each other. In contrast, diamond has a covalently bonded tetrahedral structure, which is much more rigid. As a result, graphite has higher entropy since its structure allows for greater freedom of motion for its carbon atoms. So, graphite has a greater value of S° than diamond.
02

b. Liquid and gaseous ethanol

Liquid and gaseous ethanol (C2H5OH) have the same molecular formula, but each exists in a different phase. Entropy increases when moving from solid to liquid to gas due to increased molecular freedom. Therefore, gaseous ethanol (C2H5OH(g)) has a larger value of S° than liquid ethanol (C2H5OH(l)) due to the increased degree of freedom of motion for molecules within the gas phase.
03

c. Solid and gaseous carbon dioxide

Carbon dioxide (CO2) exists as a solid (dry ice) and as a gas (familiar to us as the product of combustion and respiration). Entropy increases when moving from solid to liquid to gas. Solid CO₂ has a very ordered crystal lattice, and its molecules have limited freedom to move. In contrast, gaseous CO₂ molecules have a much higher degree of freedom and energy dispersal, as they are not held together in any definite structure. Therefore, gaseous carbon dioxide (CO₂(g)) has a greater value of S° than solid carbon dioxide (CO₂(s)).

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Most popular questions from this chapter

Choose the substance with the larger positional probability in each case. a. 1 mole of \(\mathrm{H}_{2}\) (at \(\mathrm{STP}\) ) or 1 mole of \(\mathrm{H}_{2}\) (at \(100^{\circ} \mathrm{C}, 0.5\) atm) b. 1 mole of \(\mathrm{N}_{2}\) (at \(\mathrm{STP}\) ) or 1 mole of \(\mathrm{N}_{2}\) (at \(100 \mathrm{K}, 2.0\) atm) c. 1 mole of \(\mathrm{H}_{2} \mathrm{O}(s)\) (at \(0^{\circ} \mathrm{C}\) ) or 1 mole of \(\mathrm{H}_{2} \mathrm{O}(l)\) (at \(20^{\circ} \mathrm{C}\) )

Gas \(\mathrm{A}_{2}\) reacts with gas \(\mathrm{B}_{2}\) to form gas \(\mathrm{AB}\) at a constant temperature. The bond energy of AB is much greater than that of either reactant. What can be said about the sign of \(\Delta H ? \Delta S_{\text {surr }}\) ? \(\Delta S ?\) Explain how potential energy changes for this process. Explain how random kinetic energy changes during the process.

You remember that \(\Delta G^{\circ}\) is related to \(R T \ln (K)\) but cannot remember if it's \(R T \ln (K)\) or \(-R T \ln (K) .\) Realizing what \(\Delta G^{\circ}\) and \(K\) mean, how can you figure out the correct sign?

Given the following data: $$2 \mathrm{H}_{2}(g)+\mathrm{C}(s) \longrightarrow \mathrm{CH}_{4}(g) \quad \Delta G^{\circ}=-51 \mathrm{kJ}$$ $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta G^{\circ}=-474 \mathrm{kJ}$$ $$\mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \quad \Delta G^{\circ}=-394 \mathrm{kJ}$$ Calculate \(\Delta G^{\circ}\) for \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\)

Which of the following reactions (or processes) are expected to have a negative value for \(\Delta S^{\circ} ?\) a. \(\operatorname{SiF}_{6}(a q)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{HF}(g)+\mathrm{SiF}_{4}(g)\) b. \(4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)\) c. \(\mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{COCl}_{2}(g)\) d. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) e. \(\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\)
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