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Chapter 19: Problem 89

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of

Short Answer

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(a) A solid sublimes: \(\Delta S > 0\), \(\Delta H > 0\) (b) The temperature of a sample of gas is increased at constant volume: \(\Delta S > 0\), \(\Delta H > 0\) (c) A chemical reactant is transformed into gaseous products: \(\Delta S > 0\), \(\Delta H\) depends on the specific reaction (either positive or negative).

Step by step solution

01

Process (a): A solid sublimes

When a solid undergoes sublimation (transforms directly into a gas), the entropy, or disorder, of the system increases. Therefore, 螖S is positive for this process. Sublimation is an endothermic process, meaning it absorbs heat from the surroundings. This corresponds to a positive value for 螖H. So in this case, both 螖S and 螖H are positive.
02

Process (b): The temperature of a sample of gas is increased at constant volume

When the temperature of a sample of gas increases at constant volume, the gas molecules move faster and collide with greater force, resulting in an increase in the disorder or entropy (螖S) of the system. Therefore, 螖S is positive for this process. Because the system is heating up, it absorbs heat from the surroundings. This means that the enthalpy, 螖H, is positive. So in this case, both 螖S and 螖H are positive.
03

Process (c): A chemical reactant is transformed into gaseous products

When a chemical reactant is transformed into gaseous products, the number of particles in the system typically increases, leading to a higher degree of disorder. Therefore, the entropy change, 螖S, is positive for this process. The enthalpy change, 螖H, will depend on the specifics of the reaction taking place. If it is an exothermic reaction (releases heat), then 螖H will be negative. If it is an endothermic reaction (absorbs heat), then 螖H will be positive. Without more information about the specific reaction, we cannot definitively determine the sign of 螖H for this process.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Entropy Change
Entropy, often symbolized as \( \Delta S \), is a measure of the disorder or randomness in a system. When a solid sublimes, it turns directly into a gas without passing through the liquid phase. This transformation increases the disorder because the molecules move more freely in the gaseous state compared to the structured, orderly arrangement in a solid. Therefore, the entropy change \( \Delta S \) is positive.

Here are some key points about entropy:
  • Entropy increases when a substance changes from a solid to a liquid or gas.
  • Increased temperature typically leads to an increase in entropy due to the increased motion of molecules.
  • Entropy tends to increase in any process where the system becomes more disordered.
Enthalpy Change
Enthalpy change, represented as \( \Delta H \), refers to the heat absorbed or released during a process at constant pressure. For sublimation, a solid absorbs heat to transform into a gas, making it an endothermic process. This means \( \Delta H \) is positive since heat is taken in from the surroundings.

Consider these important aspects of enthalpy:
  • If \( \Delta H \) is positive, the process is endothermic (heat absorbed).
  • If \( \Delta H \) is negative, the process is exothermic (heat released).
  • Enthalpy changes give insight into whether a process requires or releases energy.
Understanding enthalpy helps us predict whether a given reaction or phase change requires an input of energy or will release energy.
Sublimation
Sublimation is a phase transition in which a substance changes directly from a solid to a gas without passing through the liquid phase. This can happen under certain conditions of temperature and pressure, and it is frequently an endothermic process, meaning it requires the absorption of heat.

Here are some interesting points about sublimation:
  • Common examples include dry ice (solid carbon dioxide) turning to gas and the sublimation of ice under certain low pressure and temperature conditions.
  • Sublimation shows a direct increase in entropy since it moves from a more ordered (solid) to a less ordered state (gas).
  • The heat required for sublimation is known as the "heat of sublimation," contributing to the positive \( \Delta H \).
Understanding sublimation helps in comprehending how certain materials can change phases directly and what energy changes are involved in such processes.

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Most popular questions from this chapter

The \(K_{d}\) for methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) at \(25{ }^{\circ} \mathrm{C}\) is given in \(\mathrm{Ap}-\) pendix D. (a) Write the chemical equation for the equilibrium that corresponds to \(K_{b}\) (b) By using the value of \(K_{b}\), calculate \(\Delta G^{\circ}\) for the equilibrium in part (a). (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when \(\left[\mathrm{H}^{+}\right]=6.7 \times 10^{-9} \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{NH}_{3}{ }^{+}\right]=2.4 \times 10^{-3} \mathrm{M}\), and \(\left[\mathrm{CH}_{2} \mathrm{NH}_{2}\right]=0.098 \mathrm{M}\) ?

Using \(S^{\circ}\) values from Appendix C, calculate \(\Delta S^{\circ}\) values for the following reactions. In each case account for the sign of \(\Delta S^{\circ}\). (a) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\) (b) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) (c) \(\mathrm{Be}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{BeO}(s)+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(2 \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

Indicate whether cach statement is true or false. (a) The second law of thermodynamics says that entropy is conserved. (b) If the entropy of the system increases during a reversible process, the entropy change of the surroundings must decrease by the same amount. (c) In a certain spontaneous process the system undergoes an entropy change of \(4.2 \mathrm{~J} / \mathrm{K}\); therefore, the entropy change of the surroundings must be \(-4.2 \mathrm{~J} / \mathrm{K}\).

Which of the following processes are spontaneous and which are nonspontaneous: (a) the ripening of a banana, (b) dissolution of sugar in a cup of het coffee, (c) the reaction of nitrogen atoms to form \(\mathrm{N}_{2}\) molecules at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), (d) lightning. (c) formation of \(\mathrm{CH}_{4}\) and \(\mathrm{O}_{2}\) molecules from \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) at room temperature and \(1 \mathrm{~atm}\) of pressure?

] Consider a system that conststs of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (a) The two arrangements of top faces shown here can be viewed as two possible microstates of the system. Explain. (b) To which state does each microstate correspond? (c) How many possible states are there for the system? (d) Which state or states have the highest entropy? Explain. (e) Which state or states have the lowest entropy? Explain. (f) Calculate the absolute entropy of the two-dice system.
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