Textbook Question
The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (b) Calculate the value of ΔS when 60.0 g of Ga(l) solidifies at 29.8 °C.
Ch.19 - Chemical Thermodynamics
Chapter 19, Problem 26b
(b) In a particular spontaneous process the entropy of the system decreases. What can you conclude about the sign and magnitude of ΔSsurr?
Verified step by step guidance1
Identify the given information: The entropy of the system (ΔSsys) decreases, which means ΔSsys is negative.
Recall the second law of thermodynamics, which states that for a spontaneous process, the total entropy change of the universe (ΔSuniv) must be positive, i.e., ΔSuniv = ΔSsys + ΔSsurr > 0.
Since ΔSsys is negative, ΔSsurr must be positive to ensure that the sum (ΔSuniv) is positive for the process to be spontaneous.
Determine that the magnitude of ΔSsurr must be greater than the magnitude of ΔSsys to compensate for the negative ΔSsys and still achieve a positive ΔSuniv.
Conclude that ΔSsurr is positive and its magnitude is greater than the magnitude of the negative ΔSsys.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy (S)
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. For spontaneous processes, the second law of thermodynamics states that the total entropy of an isolated system must increase over time, which is crucial for understanding the behavior of systems in nature.
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Entropy in Thermodynamics
Second Law of Thermodynamics
The second law of thermodynamics states that in any spontaneous process, the total entropy of the universe (system plus surroundings) must increase. This principle implies that if the entropy of a system decreases, the entropy of the surroundings must increase by a greater amount to ensure that the overall entropy change is positive, thus driving the spontaneity of the process.
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Gibbs Free Energy (ΔG)
Gibbs free energy is a thermodynamic potential that measures the maximum reversible work obtainable from a system at constant temperature and pressure. It is defined as ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous process, linking the concepts of entropy and energy changes in chemical reactions.
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Related Practice
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
(a) Does the entropy of the surroundings increase for spontaneous processes?
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) Do you need to specify the temperature to calculate the entropy change?