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Chapter 19: Problem 32

(a) What is the difference between a state and a microstate of a system? (b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state? (c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of \(\Delta S_{\text {surr }}\) ?

Short Answer

Expert verified
(a) A state of a system refers to a set of macroscopic properties, while a microstate refers to a specific arrangement of particles exhibiting those macroscopic properties. (b) As entropy decreases, the number of microstates available to the system also decreases, meaning state A has more microstates than state B. (c) If the number of microstates decreases in a spontaneous process, then the entropy change of the system is negative, and the change in entropy of the surroundings must be positive to maintain spontaneity, making \(\Delta S_{\text{total}} \geq 0\).

Step by step solution

01

(a) State and Microstate:

A state of a system refers to a specific set of macroscopic properties such as temperature, pressure, or volume. In contrast, a microstate refers to a specific arrangement of particles in a system, describing the position and momentum of each particle, such that the system exhibits the given macroscopic properties.
02

(b) Entropy and Number of Microstates:

As the system goes from state A to state B, with its entropy decreasing, it means the number of microstates available to the system is decreasing. In other words, state A has a higher number of possible microstates compared to state B since a higher entropy implies more possible microscopic arrangements.
03

(c) Change in Surroundings' Entropy:

In a particular spontaneous process, if the number of microstates available to the system decreases, it implies that the entropy change of the system, \(\Delta S_{\text{sys}}\), is negative. However, since the process is spontaneous, it is only possible if the change in entropy of the surroundings, \(\Delta S_{\text{surr}}\), compensates for this decrease. Thus, \(\Delta S_{\text{surr}}\) must be positive, making the total change in entropy, \(\Delta S_{\text{total}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}\), greater than or equal to zero.

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Most popular questions from this chapter

(a) For a process that occurs at constant temperature, express the change in Gibbs free energy in terms of changes in the enthalpy and entropy of the system. (b) For a certain process that occurs at constant \(T\) and \(P,\) the value of \(\Delta G\) is positive. What can you conclude? (c) What is the relationship between \(\Delta G\) for a process and the rate at which it occurs?

(a) State the third law of thermodynamics. (b) Distinguish between translational motion, vibrational motion, and rotational motion of a molecule. (c) Illustrate these three kinds of motion with sketches for the HCl molecule.

Suppose we vaporize a mole of liquid water at \(25^{\circ} \mathrm{C}\) and another mole of water at \(100{ }^{\circ} \mathrm{C}\). (a) Assuming that the enthalpy of vaporization of water does not change much between \(25^{\circ} \mathrm{C}\) and \(100^{\circ} \mathrm{C},\) which process involves the larger change in entropy? (b) Does the entropy change in either process depend on whether we carry out the process reversibly or not? Explain.

The normal boiling point of \(\mathrm{Br}_{2}(l)\) is \(58.8{ }^{\circ} \mathrm{C},\) and its molar enthalpy of vaporization is \(\Delta H_{\text {vap }}=29.6 \mathrm{~kJ} /\) mol. (a) When \(\mathrm{Br}_{2}(l)\) boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when \(1.00 \mathrm{~mol}\) of \(\mathrm{Br}_{2}(l)\) is vaporized at \(58.8{ }^{\circ} \mathrm{C}\).

A certain reaction has \(\Delta H^{\circ}=+23.7 \mathrm{~kJ}\) and \(\Delta S^{\circ}=\) \(+52.4 \mathrm{~J} / \mathrm{K} .\) (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (c) Calculate \(\Delta G^{\circ}\) for the reaction at \(298 \mathrm{~K} .(\mathbf{d})\) Is the reaction spontaneous at \(298 \mathrm{~K}\) under standard conditions?
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