Question

(a) Can endothermic chemical reactions be spontaneous? (b) Can a process be spontaneous at one temperature and nonspontaneous at a different temperature? (c) Water can be decomposed to form hydrogen and oxygen, and the hydrogen and oxygen can be recombined to form water. Does this mean that the processes are thermodynamically reversible? (d) Does the amount of work that a system can doon its Id on the nath of the nrocese?

Short answer

(a) Yes, endothermic chemical reactions can be spontaneous if the increase in entropy (\( ∆S \)) is large enough to overcome the positive enthalpy change (\( ∆H \)), resulting in a negative Gibbs free energy (\( ∆G \)). This is more likely to occur at higher temperatures due to the temperature-entropy term in the Gibbs free energy equation. (b) Yes, a process can be spontaneous at one temperature and nonspontaneous at a different temperature, as the Gibbs free energy (\( ∆G \)) is influenced by both enthalpy (\( ∆H \)) and entropy (\( ∆S \)) changes, as well as temperature (T). (c) The decomposition and recombination of water into hydrogen and oxygen are not thermodynamically reversible processes, as they have finite rates and energy losses and cannot fully reverse with no change to the system and its surroundings. (d) Yes, the amount of work that a system can do depends on the path of the process. Different process paths can lead to different conversion efficiencies and energy available for work, resulting in different amounts of work being done for the same initial and final states of a system.

Step-by-step solution

(Question a: Endothermic Spontaneity)

(An endothermic reaction is one where energy is absorbed from the surroundings during the reaction. Spontaneity refers to whether a reaction will occur on its own without any external intervention. For a reaction to be spontaneous, its Gibbs free energy (\( ∆G \)) must be negative. The key to answering this question is to recall the relationship between Gibbs free energy (\( ∆G \)), entropy (\( ∆S \)), and enthalpy (\( ∆H \)): \[ ∆G = ∆H - T∆S \] where T is the temperature in Kelvin.)

(Answer a: Endothermic Spontaneity)

(Yes, endothermic chemical reactions can be spontaneous if the increase in entropy (\( ∆S \)) is large enough to overcome the positive enthalpy change (\( ∆H \)), resulting in a negative Gibbs free energy (\( ∆G \)). This is more likely to occur at higher temperatures since the entropy term is multiplied by the temperature (T) in the Gibbs free energy equation.)

(Question b: Spontaneity and Temperature)

(This question focuses on understanding whether a process can have different spontaneity characteristics at different temperatures. To answer this question, we need to consider how the relation between Gibbs free energy (\( ∆G \)), entropy (\( ∆S \)), and enthalpy (\( ∆H \)) can be affected by changes in temperature.)

(Answer b: Spontaneity and Temperature)

(Yes, a process can be spontaneous at one temperature and nonspontaneous at a different temperature. This is because the Gibbs free energy (\( ∆G \)) is influenced by both enthalpy (\( ∆H \)) and entropy (\( ∆S \)) changes, as well as temperature (T). As temperature changes, the contribution from the temperature-entropy term (\( T∆S \)) in the \( ∆G = ∆H - T∆S \) equation can change the overall sign of Gibbs free energy, leading to a change in spontaneity.)

(Question c: Reversible Processes)

(This question asks whether water decomposition and recombination processes are thermodynamically reversible or not. To answer this, we need to understand the concept of thermodynamic reversibility and how it relates to the given processes.)

(Answer c: Reversible Processes)

(Although water can be decomposed into hydrogen and oxygen, and hydrogen and oxygen can be recombined to form water, this does not mean that both processes are thermodynamically reversible. A thermodynamically reversible process is an idealized process that occurs infinitely slowly and can be reversed with no change to the system and its surroundings. The decomposition and recombination of water are real processes with finite rates and energy losses; therefore, they are not thermodynamically reversible processes.)

(Question d: Work Done on the System)

(The question asks about the dependency of the amount of work that a system can do on the path of the process. The answer lies in understanding the relationship between work, energy, and the specifics of a system's path in a process.)

(Answer d: Work Done on the System)

(Yes, the amount of work that a system can do depends on the path of the process. A system can do work when it converts internal energy into other forms of energy. However, the conversion efficiency and the energy available to do work can differ for different process paths, resulting in different amounts of work being done for the same initial and final states of a system.)

Key concepts

Endothermic Reactions

Endothermic reactions are processes where heat is absorbed from the surroundings into the reacting system. In such reactions, the enthalpy change (\( \Delta H \)) is positive because energy input is required. A common example of an endothermic reaction is the melting of ice. Now, you might wonder whether endothermic reactions can occur spontaneously. The answer depends on Gibbs free energy (\( \Delta G \)).
According to the formula:\[\Delta G = \Delta H - T\Delta S\]spontaneity is achieved when\( \Delta G \)is negative. In endothermic reactions, if the increase in entropy (\( \Delta S \)) is significant and the temperature (T) is high enough, it can make\( \Delta G \)negative, thus making the reaction spontaneous. This is why endothermic reactions like ice melting appear spontaneous under specific conditions.

Thermodynamic Spontaneity

Thermodynamic spontaneity is a measure of whether a process can occur on its own without needing external energy. For understanding this concept, Gibbs free energy is crucial. The spontaneity of a process is predicted by the Gibbs free energy equation, \( \Delta G = \Delta H - T\Delta S \). If\( \Delta G \)is negative, the process will proceed spontaneously.
Conditions such as temperature and entropy greatly influence spontaneity. A process can be spontaneous at one temperature and not at another due to changes in the entropy term \( T\Delta S \). As temperature varies, it alters the contribution from entropy, thus changing \( \Delta G \)and the overall spontaneity. This is why the melting of ice is spontaneous at temperatures above 0°C but not below.

Reversible Processes

Reversible processes are theoretical constructs in thermodynamics where a process can be reversed without leaving any net change in both the system and its surroundings. These processes occur infinitely slowly, allowing the system to remain in equilibrium at all times.
In reality, truly reversible processes don't exist because they require an infinite amount of time. Take, for example, the decomposition of water into hydrogen and oxygen. While these gases can be recombined to form water, such processes aren’t reversible in the thermodynamic sense. This is due to energy dissipation as heat, which leads to irreversible changes in the surroundings. Hence, while conceptually handy, true reversibility remains a theoretical ideal, not practically achievable.

Work in Thermodynamics

Work in thermodynamics refers to the energy transfer that takes place when a system undergoes a change due to an external influence. The amount of work done by or on a system during a thermodynamic process depends greatly on the path taken by the process.
In simple terms, it’s not just about the initial and final states but how the system gets from one to the other. Different process paths can lead to different amounts of work being done even if the start and end states are the same. For instance, in a gas expansion process, the work done can differ if the expansion is rapid or slow due to varying pressure conditions throughout the process. Understanding path dependency is key in evaluating the efficiency of thermodynamic processes and systems.