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Chapter 19: Problem 38

How does the entropy of the system change when (a) the temperature of the system increases, (b) the volume of a gas increases, \((c)\) equal volumes of ethanol and water are mixed to form a solution?

Short Answer

Expert verified
(a) When the temperature of a system increases, the entropy generally increases, as particles gain kinetic energy and move more randomly, leading to higher disorder. (b) The entropy of a system increases when the volume of a gas increases, as the increased volume allows for more possible arrangements and disorder among gas particles. (c) The entropy of a system increases when equal volumes of ethanol and water are mixed, as the mixing creates a greater number of molecular configurations, leading to higher disorder.

Step by step solution

01

(a) Temperature Increase

When the temperature of a system increases, the entropy of the system generally increases. Entropy is the measure of the degree of disorder/randomness in a system. As the temperature increases, the particles in the system gain kinetic energy and start moving more rapidly, leading to a higher degree of disorder. Consequently, the entropy increases due to increasing temperature.
02

(b) Volume Increase of a Gas

When the volume available to a gas increases, the gas particles have more space to disperse throughout. The increased volume allows for more possible arrangements of gas particles, leading to a higher degree of disorder in the system. As the disorder increases, so does the entropy of the system. Thus, when the volume of a gas increases, the entropy of the system also increases.
03

(c) Mixing Ethanol and Water

When equal volumes of ethanol and water are mixed together to form a solution, the entropy of the resulting solution is greater compared to the entropy of the individual components (ethanol and water) when separated. This is because mixing the two liquids creates a greater number of possible configurations for the molecules in the system, leading to a higher level of disorder. Consequently, the entropy of the system increases when ethanol and water are mixed together to form a solution.

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Most popular questions from this chapter

(a) How can we calculate \(\Delta S\) for an isothermal process? (b) Does \(\Delta S\) for a process depend on the path taken from the initial state to the final state of the system? Explain.

(a) What is special about a reversible process? (b) Suppose a reversible process is reversed, restoring the system to its original state. What can be said about the surroundings after the process is reversed? (c) Under what circumstances will the vaporization of water to steam be a reversible process? (d) Are any of the processes that occur in the world around us reversible in nature? Explain.

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) or \(\mathrm{C}_{2} \mathrm{H}_{6}(g),(\mathbf{b}) \mathrm{CO}_{2}(g)\) or \(\mathrm{CO}(g) ?\) Explain.

For each of the following pairs, indicate which substance possesses the larger standard entropy: (a) \(1 \mathrm{~mol}\) of \(\mathrm{P}_{4}(g)\) at \(300^{\circ} \mathrm{C}, 0.01 \mathrm{~atm},\) or \(1 \mathrm{~mol}\) of \(\mathrm{As}_{4}(g)\) at \(300^{\circ} \mathrm{C}, 0.01 \mathrm{~atm} ;\) (b) \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at \(100^{\circ} \mathrm{C}, 1 \mathrm{~atm},\) or \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(l)\) at \(100^{\circ} \mathrm{C}, 1 \mathrm{~atm} ;\) (c) \(0.5 \mathrm{~mol}\) of \(\mathrm{N}_{2}(g)\) at \(298 \mathrm{~K}, 20-\mathrm{L}\) volume, or \(0.5 \mathrm{~mol} \mathrm{CH}_{4}(g)\) at \(298 \mathrm{~K}, 20-\mathrm{L}\) volume; (d) \(100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or \(100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\) at \(30^{\circ} \mathrm{C}\)

For a certain chemical reaction, \(\Delta H^{\circ}=-35.4 \mathrm{~kJ}\) and \(\Delta S^{\circ}=-85.5 \mathrm{~J} / \mathrm{K} .\) (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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