Question

Is \(\Delta S_{\text {surr }}\) favorable or unfavorable for exothermic reactions? Endothermic reactions? Explain.

Short answer

For exothermic reactions, \(\Delta S_{\text{surr}}\) is positive, indicating an increase in the entropy of the surroundings, which is considered favorable. On the other hand, for endothermic reactions, \(\Delta S_{\text{surr}}\) is negative, indicating a decrease in the entropy of the surroundings, which is considered unfavorable.

Step-by-step solution

Define entropy

Entropy, represented as \(S\), is a measure of the degree of disorder or randomness in a system. An increase in entropy generally means a higher degree of disorder, while a decrease in entropy indicates a lower degree of disorder.

Calculate the change in entropy of the surroundings

For chemical reactions, the change in entropy of the surroundings, denoted as \(\Delta S_{\text{surr}}\), can be calculated using the relation: \begin{equation} \Delta S_{\text{surr}} = - \dfrac{q_{\text{sys}}}{T} \end{equation} where \(q_{\text{sys}}\) is the heat flow of the system, which is positive if the system absorbs heat (endothermic) and negative if the system releases heat (exothermic), and \(T\) is the temperature in Kelvin.

Analyze the change in entropy of surroundings for exothermic reactions

In an exothermic reaction, heat is released into the surroundings, so \(q_{\text{sys}}\) is negative. Therefore, when we plug this into the equation: \begin{equation} \Delta S_{\text{surr}} = - \dfrac{-q_{\text{sys}}}{T} \end{equation} Since both the numerator and denominator are positive, \(\Delta S_{\text{surr}}\) will be positive, meaning the entropy of the surroundings increases.

Analyze the change in entropy of surroundings for endothermic reactions

In an endothermic reaction, heat is absorbed from the surroundings, so \(q_{\text{sys}}\) is positive. Therefore, when we plug this into the equation: \begin{equation} \Delta S_{\text{surr}} = - \dfrac{q_{\text{sys}}}{T} \end{equation} Since the numerator is positive and the denominator is positive, \(\Delta S_{\text{surr}}\) will be negative, meaning the entropy of the surroundings decreases.

Conclude whether the change in entropy of the surroundings is favorable or unfavorable

From the analysis in Steps 3 and 4, we can conclude that: - For exothermic reactions, \(\Delta S_{\text{surr}}\) is positive, which indicates an increase in the entropy of the surroundings. Entropy increasing is generally considered favorable because it leads to a more dispersed and disordered state. - For endothermic reactions, \(\Delta S_{\text{surr}}\) is negative, indicating a decrease in the entropy of the surroundings, which is generally considered unfavorable because it leads to a less dispersed and more ordered state.

Key concepts

Exothermic Reactions

Exothermic reactions are processes where heat is released into the surroundings. This type of reaction is characterized by the system losing energy as it transfers heat to its environment. A classic example of an exothermic reaction is combustion, like burning wood or fossil fuels.

When such reactions occur, the energy emitted increases the thermal energy of the surroundings, which has a direct impact on the entropy of the surroundings. Entropy, a concept in thermodynamics, relates to the level of disorder or randomness. In the case of an exothermic reaction, since the system releases energy (making the heat flow of the system, \(q_{\text{sys}}\), negative), the surroundings absorb this heat.

The change of entropy for the surroundings, \(\Delta S_{\text{surr}}\), is calculated using the formula:

• \(\Delta S_{\text{surr}} = - \dfrac{q_{\text{sys}}}{T}\)

Here, a negative \(q_{\text{sys}}\) results in a positive change in entropy for the surroundings. This positive increase implies more disorder, which is typically favorable as systems naturally progress towards more random states. Thus, exothermic reactions contribute to increasing the entropy of their environment.

Endothermic Reactions

Endothermic reactions are processes where the system absorbs heat from its surroundings. These reactions require input of energy, which causes the surroundings to become cooler. A good example of an endothermic process is the melting of ice into water.

For these reactions, the heat flow, \(q_{\text{sys}}\), is positive as the system takes in energy. This absorption reduces the thermal energy available in the surroundings, affecting the entropy negatively.

• The change in entropy of the surroundings for an endothermic reaction is given by:
• \(\Delta S_{\text{surr}} = - \dfrac{q_{\text{sys}}}{T}\)

Since \(q_{\text{sys}}\) is positive in endothermic reactions, \(\Delta S_{\text{surr}}\) becomes negative. This decrease in entropy is often deemed unfavorable, as it indicates a move towards a more ordered state, contradicting the natural tendency towards disorder. Therefore, endothermic reactions result in a lowering of the entropy of the surroundings.

Entropy Change of Surroundings

The entropy change of the surroundings, represented as \(\Delta S_{\text{surr}}\), plays an essential role in understanding chemical reactions. It measures how the heat exchanged between the system and its environment impacts the latter's disorder or randomness. This value helps in predicting the favorability of reactions based on their thermal interactions with their surroundings.

For both exothermic and endothermic reactions, the entropy change of the surroundings is calculated using the equation:

• \(\Delta S_{\text{surr}} = - \dfrac{q_{\text{sys}}}{T}\)

This equation reveals that the sign and magnitude of \(\Delta S_{\text{surr}}\) are inversely related to the heat flow of the system.
- In exothermic reactions, where heat is released, \(\Delta S_{\text{surr}}\) is positive, indicating increased disorder.- In endothermic reactions, where heat is absorbed, \(\Delta S_{\text{surr}}\) is negative, pointing to decreased disorder.Understanding whether \(\Delta S_{\text{surr}}\) is favorable or unfavorable is crucial in assessing how these reactions influence the overall entropy change, \(\Delta S_{\text{universe}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}\), and therefore their spontaneity and feasibility.