Chapter 6: Problem 53
A mong the following, the wrong statement is (1) Entropy decreases during the crystallization of a solute from solution. (2) At a certain temperuture \(T\), the endothermic reaction \(\mathrm{A} \rightarrow \mathrm{B}\) proceeds almost to completion if \(\Delta S>0\).(3) In a spontaneous irreversible process the total entropy of the system and surroundings increases. (4) When the value of entropy is greater, then the ability to work is minimum,
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Second Law of Thermodynamics
The Second Law of Thermodynamics is a fundamental principle in physics and chemistry. It states that the total entropy of an isolated system will never decrease over time; it will either increase or remain constant. This means that natural processes tend to move towards a state of greater disorder or randomness.
For instance, when you leave a hot cup of coffee in a room, it will gradually cool down until it reaches room temperature. This process happens spontaneously, meaning it doesn't need external energy to proceed. During this cooling process, the entropy of the coffee and its surroundings increases.
If we consider spontaneous chemical reactions, the Second Law of Thermodynamics helps us understand why certain reactions occur without external intervention. This not only applies to chemical systems but is also a universal concept applicable to all physical processes.
For instance, when you leave a hot cup of coffee in a room, it will gradually cool down until it reaches room temperature. This process happens spontaneously, meaning it doesn't need external energy to proceed. During this cooling process, the entropy of the coffee and its surroundings increases.
If we consider spontaneous chemical reactions, the Second Law of Thermodynamics helps us understand why certain reactions occur without external intervention. This not only applies to chemical systems but is also a universal concept applicable to all physical processes.
Entropy Change
Entropy change, denoted by \(\text{ΔS}\), indicates the change in entropy during a process. When a system transitions from one state to another, the entropy change accompanies this shift. If \(\text{ΔS} > 0\), it means the disorder of the system is increasing, which often aligns with the likelihood of the process occurring spontaneously.
For example, if a reaction goes from reactants to products and produces gas, the entropy typically increases because gases have more disorder than liquids or solids. This can be modeled using the equation:
\[ \text{ΔG} = \text{ΔH} - T\text{ΔS} \]
Here, \(\text{ΔG}\) is the change in Gibbs free energy, \(\text{ΔH}\) is the change in enthalpy, and \(\text{ΔS}\) is the change in entropy. This equation is crucial in determining whether a process is spontaneous or not.
For example, if a reaction goes from reactants to products and produces gas, the entropy typically increases because gases have more disorder than liquids or solids. This can be modeled using the equation:
\[ \text{ΔG} = \text{ΔH} - T\text{ΔS} \]
Here, \(\text{ΔG}\) is the change in Gibbs free energy, \(\text{ΔH}\) is the change in enthalpy, and \(\text{ΔS}\) is the change in entropy. This equation is crucial in determining whether a process is spontaneous or not.
Spontaneous Process
A spontaneous process is one that occurs naturally without any external energy input. Think of ice melting into water at room temperature: it happens on its own. In thermodynamics, a process is considered spontaneous if it leads to an increase in the total entropy of the system and its surroundings.
According to the Gibbs free energy equation, for a process to be spontaneous at constant temperature and pressure, the change in Gibbs free energy \(\text{ΔG}\) must be negative. This can be seen in the equation:
\[ \text{ΔG} = \text{ΔH} - T\text{ΔS} \]
When \(\text{ΔS}\) is positive and \(\text{ΔH}\) is negative, \(\text{ΔG}\) will likely be negative, indicating a spontaneous process. For an endothermic reaction where \(\text{ΔH}\) is positive, the process may still be spontaneous if the temperature is high enough to make \(\text{TΔS}\) larger than \(\text{ΔH}\).
According to the Gibbs free energy equation, for a process to be spontaneous at constant temperature and pressure, the change in Gibbs free energy \(\text{ΔG}\) must be negative. This can be seen in the equation:
\[ \text{ΔG} = \text{ΔH} - T\text{ΔS} \]
When \(\text{ΔS}\) is positive and \(\text{ΔH}\) is negative, \(\text{ΔG}\) will likely be negative, indicating a spontaneous process. For an endothermic reaction where \(\text{ΔH}\) is positive, the process may still be spontaneous if the temperature is high enough to make \(\text{TΔS}\) larger than \(\text{ΔH}\).
Gibbs Free Energy
Gibbs free energy, denoted as \(\text{G}\), is a crucial concept in determining the spontaneity of a process. It combines enthalpy (heat content) and entropy (degree of disorder) of a system to predict whether a reaction will occur on its own. The formula is:
\[ \text{ΔG} = \text{ΔH} - T\text{ΔS} \]
In this equation, \(\text{ΔH}\) represents the change in enthalpy, \(\text{ΔS}\) represents the change in entropy, and \(\text{T}\) is the temperature in Kelvin.
When \(\text{ΔG}\) is negative, the reaction is spontaneous. This means it can occur without external energy. If \(\text{ΔG}\) is positive, the reaction is non-spontaneous, and will require energy input to proceed. When \(\text{ΔG} = 0\), the system is in equilibrium, and no net change occurs.
Thus, Gibbs free energy is a comprehensive indicator that helps predict the feasibility of reactions under constant temperature and pressure conditions.
\[ \text{ΔG} = \text{ΔH} - T\text{ΔS} \]
In this equation, \(\text{ΔH}\) represents the change in enthalpy, \(\text{ΔS}\) represents the change in entropy, and \(\text{T}\) is the temperature in Kelvin.
When \(\text{ΔG}\) is negative, the reaction is spontaneous. This means it can occur without external energy. If \(\text{ΔG}\) is positive, the reaction is non-spontaneous, and will require energy input to proceed. When \(\text{ΔG} = 0\), the system is in equilibrium, and no net change occurs.
Thus, Gibbs free energy is a comprehensive indicator that helps predict the feasibility of reactions under constant temperature and pressure conditions.
