Textbook Question
All the oxides of nitrogen have positive values of ΔG°f at 298 K, but only one common oxide of nitrogen has a positive ΔS°f. Identify that oxide of nitrogen without reference to thermodynamic data and explain.
Ch.19 - Free Energy & Thermodynamics
Chapter 19, Problem 99
Is the sign of ΔSuniv for each process positive or negative? Explain for the following: b. the electrolysis of H2O(l) to H2(g) and O2(g) at 298 K c. the growth of an oak tree from a little acorn.
Verified step by step guidance1
insert step 1> Identify the processes involved in each scenario. For part b, the process is the electrolysis of water, and for part c, it is the growth of an oak tree from an acorn.
insert step 2> Recall the second law of thermodynamics, which states that the entropy of the universe (ΔS_{univ}) increases for spontaneous processes.
insert step 3> For part b, consider the electrolysis of water: 2H_2O(l) \rightarrow 2H_2(g) + O_2(g). This process involves breaking bonds in water molecules to form hydrogen and oxygen gases, which increases the disorder or entropy of the system.
insert step 4> For part c, consider the growth of an oak tree: This process involves organizing simple molecules into complex structures, which decreases the entropy of the system. However, the overall entropy change of the universe must be considered, including the surroundings.
insert step 5> Determine the sign of ΔS_{univ} for each process by considering the changes in entropy of the system and surroundings. For part b, the increase in gas molecules suggests a positive ΔS_{univ}. For part c, the decrease in system entropy is offset by energy exchanges with the surroundings, potentially leading to a positive ΔS_{univ} if the process is spontaneous.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Entropy (ΔS)
Entropy is a measure of the disorder or randomness in a system. In thermodynamics, the change in entropy (ΔS) can indicate whether a process is spontaneous. A positive ΔS suggests an increase in disorder, while a negative ΔS indicates a decrease in disorder. Understanding how entropy changes during a process is crucial for determining the sign of ΔSuniv.
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Entropy in Thermodynamics
Second Law of Thermodynamics
The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time. It implies that natural processes tend to move towards a state of maximum disorder or entropy. This law is essential for analyzing processes like electrolysis and biological growth, as it helps predict whether the overall entropy change (ΔSuniv) will be positive or negative.
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Spontaneity of Processes
A process is considered spontaneous if it occurs without external intervention, often associated with a positive change in the universe's entropy (ΔSuniv > 0). For the electrolysis of water, the process is non-spontaneous under standard conditions, while the growth of an oak tree is a spontaneous biological process. Evaluating spontaneity involves analyzing both the system and surroundings to determine the overall entropy change.
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Related Practice
Textbook Question
The values of ΔG°f for the hydrogen halides become less negative with increasing atomic number. The ΔG°f of HI is slightly positive. However, the trend in ΔS°f is to become more positive with increasing atomic number. Explain.
Textbook Question
Indicate and explain the sign of ΔSuniv for each process. a. 2 H2(g) + O2(g) → 2 H2O (l) at 298 K.
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Textbook Question
A metal salt with the formula MCl2 crystallizes from water to form a solid with the composition MCl2 • 6 H2O. The equilibrium vapor pressure of water above this solid at 298 K is 18.3 mmHg. What is the value of ΔG for the reaction MCl2 • 6 H2O(s) ⇌ MCl2(s) + 6 H2O(g) when the pressure of water vapor is 18.3 mmHg? When the pressure of water vapor is 760 mmHg?
Textbook Question
The solubility of AgCl(s) in water at 25 °C is 1.33⨉10-5 mol/L and its ΔH° of solution is 65.7 kJ/mol. What is its solubility at 50.0 °C?