(a) Does the entropy of the surroundings increase for spontaneous processes?

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Understand that entropy is a measure of disorder or randomness in a system.

Recall the Second Law of Thermodynamics, which states that for any spontaneous process, the total entropy of the universe (system plus surroundings) always increases.

Recognize that the universe's entropy change (ΔS_universe) is the sum of the entropy change of the system (ΔS_system) and the entropy change of the surroundings (ΔS_surroundings).

For a process to be spontaneous, ΔS_universe = ΔS_system + ΔS_surroundings > 0.

Therefore, if the system's entropy decreases, the surroundings' entropy must increase by a greater amount to ensure that the total entropy change is positive, confirming that the entropy of the surroundings increases for spontaneous processes.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of ways a system can be arranged, with higher entropy indicating greater disorder. Understanding entropy is crucial for analyzing spontaneous processes, as they tend to increase the overall entropy of the universe.

Spontaneous Processes

A spontaneous process is a reaction or change that occurs without external intervention. These processes are characterized by a decrease in the free energy of the system, often leading to an increase in the entropy of the universe. Recognizing the conditions under which a process is spontaneous helps in predicting the direction of chemical reactions.

Second Law of Thermodynamics

The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time. For a process to be spontaneous, the entropy of the universe (the system plus surroundings) must increase. This principle is fundamental in determining whether the entropy of the surroundings increases during a spontaneous process.

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Textbook Question

The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔH_fus = 5.59 kJ/mol. (a) When molten gallium solidifies to Ga(s) at its normal melting point, is ΔS positive or negative?

Textbook Question

The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔH_fus = 5.59 kJ/mol. (b) Calculate the value of ΔS when 60.0 g of Ga(l) solidifies at 29.8 °C.

Textbook Question

Indicate whether each statement is true or false. (c) In a certain spontaneous process the system undergoes an entropy change of 4.2 J/K; therefore, the entropy change of the surroundings must be -4.2 J/K.

Textbook Question

(b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of ΔS_surr?

Textbook Question

(c) During a certain reversible process, the surroundings undergo an entropy change, ΔSsurr = -78 J/K. What is the entropy change of the system for this process?

Textbook Question

(a) What sign for Δ𝑆 do you expect when the pressure on 0.600 mol of an ideal gas at 350 K is increased isothermally from an initial pressure of 0.750 atm?

(b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process.

(c) Which of the following statements about this process are true? (i) The entropy change you calculated will be the same for at any other constant temperature. (ii) The value of Δ𝑆 you calculated is valid only if the compression is done irreversibly. (iii) If the number of moles of gas being compressed were decreased by a factor of three, the entropy change would increase by a factor of three.