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 do on its surroundings depend on the path of the process?

Short answer

(a) Yes, endothermic chemical reactions can be spontaneous if the entropy change (∆S) is positive and large enough, causing ∆G to be negative at certain temperatures. (b) A process can be spontaneous at one temperature and nonspontaneous at another temperature due to changes in the Gibbs free energy (∆G) as temperature changes. (c) The decomposition and recombination of water does not necessarily mean these processes are thermodynamically reversible; conditions for reversibility must be met. (d) The amount of work that a system can do on its surroundings depends on the path of the process, as work and heat transferred differ depending on the specific path taken between initial and final states.

Step-by-step solution

Answer (a)

Yes, endothermic chemical reactions can be spontaneous. The spontaneity of a reaction depends on the Gibbs free energy change (∆G), which is defined as ∆G = ∆H - T∆S, where ∆H is the enthalpy change, T is temperature, and ∆S is the entropy change. A reaction is spontaneous if ∆G is negative. Endothermic reactions have a positive ∆H; however, if the entropy change (∆S) is positive and large enough, the reaction will be spontaneous at certain temperatures.

Answer (b)

Yes, a process can be spontaneous at one temperature and nonspontaneous at another temperature. This is because the spontaneity of a process is determined by the Gibbs free energy change (∆G), which is dependent on both the enthalpy change (∆H) and the entropy change (∆S), as well as the temperature (T). As the temperature changes, the terms T∆S and ∆H in the equation ∆G = ∆H - T∆S can have different magnitudes and signs, causing the value of ∆G to change. If ∆G is negative, the process is spontaneous, and if ∆G is positive, the process is nonspontaneous.

Answer (c)

The decomposition of water into hydrogen and oxygen, and the recombination of hydrogen and oxygen into water, can be considered as two different processes. Just because these two processes can occur does not necessarily mean that they are thermodynamically reversible. In a thermodynamically reversible process, the system is in equilibrium with its surroundings throughout the process, and a small change in a variable can reverse the process. For the water decomposition and recombination processes to be thermodynamically reversible, the conditions for reversibility must be met, which is not always the case in reality.

Answer (d)

Yes, the amount of work that a system can do on its surroundings depends on the path of the process. Work, heat, and internal energy are state functions that depend on the initial and final states of the system. However, the amounts of work and heat transferred differ depending on the specific path taken between those states. A system might do more work along one path than another, even if the initial and final states are the same. For example, during an isothermal expansion, the work done by an ideal gas on its surroundings depends on whether the expansion occurs reversibly or irreversibly.

Key concepts

Endothermic Reactions and Spontaneity

Endothermic reactions are chemical processes in which heat is absorbed from the surroundings. Despite this absorption of energy, some of these reactions can still be spontaneous. Spontaneity in chemistry refers to a reaction's tendency to occur without external influence. A spontaneous reaction is favored thermodynamically when the Gibbs Free Energy (\( \Delta G \)) is negative. Using the formula \( \Delta G = \Delta H - T\Delta S \), spontaneity depends on:

• Enthalpy change (\( \Delta H \)): Endothermic reactions have a positive \( \Delta H \) because they absorb energy.
• Entropy change (\( \Delta S \)): A positive increase in disorder can drive a reaction to spontaneity.
• Temperature (\( T \)): Higher temperatures can favor entropy-driven reactions.

If \( \Delta S \) is large and positive, and temperature is high enough, then \( \Delta G \) becomes negative, rendering an endothermic reaction spontaneous.

Spontaneity and Temperature Variations

The concept of spontaneity is closely linked to temperature. A reaction that is spontaneous at one temperature might be nonspontaneous at another. This is due to the role temperature plays in the Gibbs Free Energy equation \( \Delta G = \Delta H - T\Delta S \). Temperature (\( T \)) directly affects the term \( T\Delta S \). For instance:

• Low temperatures might hinder spontaneity if the \( \Delta S \) is not significantly positive.
• High temperatures can enhance the effect of \( \Delta S \), potentially making a reaction spontaneous even if it involves a positive \( \Delta H \).
• The balance between entropy and enthalpy shifts with temperature, affecting spontaneity.

This temperature dependency is why some processes may only be feasible at certain temperature ranges.

Understanding Thermodynamic Processes

Thermodynamic processes describe the pathway from start to finish of a reaction or physical change. These processes can vary widely as they might employ different conditions and pathways. Some processes appear reversible under specific conditions, meaning they could ideally revert to their original state without external influence. However, true thermodynamic reversibility is rare, as it requires an infinitesimally slow process, maintaining equilibrium throughout:

• Reversible processes mean both forward and backward changes occur without a net gain or loss of energy.
• Real processes often have inefficiencies, like friction or energy dissipation, hindering reversibility.
• Examples like water decomposition and recombination showcase how apparent reversibility requires precise control to align with thermodynamic standards.

Though illustrative, reversible processes are more of a theoretical ideal than a practical norm.

The Role of Entropy Change

Entropy (\( \Delta S \)) represents the degree of randomness or disorder in a system. It's an integral part of determining a system's spontaneity. An increase in entropy often coincides with spontaneous processes. In the formula \( \Delta G = \Delta H - T\Delta S \):

• A positive \( \Delta S \), or increase in disorder, contributes to a negative \( \Delta G \), which favors spontaneity.
• The greater the entropy increase, the more likely a reaction is to proceed without external energy input, especially at high temperatures.
• Entropy quantifies the spread of energy throughout a system, promoting states with the most dispelled energy as likely outcomes.

Thus, an understanding of entropy helps predict when and why reactions occur, highlighting the importance of this thermodynamic principle.