Problem 14 - Chemistry The Central Science In Si Units

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?

Step-by-Step Solution

Answer

Yes, (a) endothermic reactions can be spontaneous. (b) A process can be spontaneous at one temperature and nonspontaneous at another. (c) Water decomposition is not thermodynamically reversible. (d) The work done depends on the path.

Step 1: Understanding Endothermic Reactions

Endothermic reactions absorb heat from their surroundings. These reactions can be spontaneous if the increase in entropy (disorder) of the system and surroundings is greater than the total energy absorbed. It aligns with Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \). If \( \Delta G < 0 \), the reaction is spontaneous.

Step 2: Temperature's Role in Spontaneity

The spontaneity of a process can depend on temperature. A reaction may be spontaneous at a certain temperature if the Gibbs free energy is negative, and nonspontaneous at another if the sign reverses. For instance, the melting of ice is spontaneous above 0°C but nonspontaneous below it.

Step 3: Reversibility of Water Decomposition

Reversibility in thermodynamics refers to a process that can return to its initial state without leaving changes in the surroundings. Although water can be decomposed into hydrogen and oxygen, and vice versa, these processes involve energy changes and are not perfectly reversible due to energy losses as heat.

Step 4: Path Dependence of Work

Work depends on the path taken in thermodynamic processes. For example, work done by a gas when expanding depends on whether the expansion is controlled slowly or done rapidly and unrestrained. Different paths result in different amounts of work being done.

Key Concepts

Endothermic Reactions

Endothermic reactions are fascinating because they require the absorption of heat from their surroundings.
These reactions tend to feel cold to the touch because they pull in heat energy to proceed.
In terms of thermodynamics, they possess a positive enthalpy change (ΔH > 0).
Although it seems counterintuitive, endothermic reactions can indeed be spontaneous. This happens when the entropy (disorder) of the system and surroundings increases enough to drive the reaction forward.
The key factor here is the balance dictated by the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \).
In this equation:

• \( \Delta G \) is Gibbs free energy change,
• \( \Delta H \) is the enthalpy change,
• \( T \) is the temperature in Kelvin,
• \( \Delta S \) is the change in entropy.

For a reaction to be spontaneous, the Gibbs free energy change must be negative. This can occur even if \( \Delta H \) is positive, provided the term \( T \Delta S \) is sufficiently larger to make \( \Delta G < 0 \).

Spontaneity

Spontaneity in chemical reactions can often be a puzzling concept because it doesn't necessarily mean a reaction occurs quickly or without activation energy.
In thermodynamics, a process is considered spontaneous if it can occur without continuous input of energy from outside the system.
Whether a reaction is spontaneous or not highly depends on its Gibbs free energy. The driving force of spontaneity means the system naturally progresses towards a state with lower free energy.
This is why we consider the sign of \( \Delta G \).

• If \( \Delta G < 0 \), the process is spontaneous.
• If \( \Delta G > 0 \), the process is non-spontaneous.

Temperature plays a crucial role in spontaneity. Consider a reaction that is nonspontaneous at low temperatures but becomes spontaneous at higher temperatures due to a change in entropy overriding the enthalpy change.
A classic example is the melting of ice into water, which is spontaneous above 0°C but not below this temperature.

Entropy

Entropy is a measure of disorder or randomness in a system.
In thermodynamics, it reflects how energy disperses in a process.
When a process results in a higher spread of energy, it leads to an increase in entropy. This is often seen as a natural drive for most chemical reactions, as systems tend to move from states of low entropy to high entropy.
Entropy change, \( \Delta S \), significantly impacts the Gibbs free energy equation, particularly in influencing the spontaneity of reactions. The more disorder or randomness created, the more it helps in offsetting the energy required, potentially making an endothermic reaction spontaneous.
One intriguing aspect of entropy is that it's not just determined by the movements of individual particles, but also how these particles interact and arrange themselves over time.
Thus, understanding entropy helps in comprehending why certain processes occur the way they do, guiding us through the paths taken to reach equilibrium.

Gibbs Free Energy

Gibbs free energy is a fundamental concept in thermodynamics, serving as a criterion for spontaneity of processes at constant pressure and temperature.
The concept is crucial because it provides a clear and straightforward predictor of whether a reaction will occur as written.Expressed with the equation \( \Delta G = \Delta H - T \Delta S \), it brings together enthalpic and entropic components to account for both heat transfer and disorder.
*Key Components of Gibbs Free Energy Equation:*

• \( \Delta G \): Change in free energy, indicates spontaneity.
• \( \Delta H \): Change in enthalpy, shows heat absorbed or released.
• \( T \): Temperature in Kelvin.
• \( \Delta S \): Change in entropy, represents system disorder.

When analyzing reactions:- A negative \( \Delta G \) implies the reaction proceeds spontaneously under set conditions.- A positive \( \Delta G \) indicates nonspontaneity, requiring external energy.Ultimately, Gibbs free energy serves as a valuable tool for chemists and physicists to predict chemical behavior and the feasibility of reactions.