Question

Decide whether each of the following statements is true or false. If false, rewrite it to make it true. (a) The entropy of a substance increases on going from the liquid to the vapor state at any temperature. (b) An exothermic reaction will always be spontaneous. (c) Reactions with a positive \(\Delta_{\mathrm{r}} H^{\circ}\) and a positive \(\Delta_{\mathrm{r}} S^{\circ}\) can never be product-favored. (d) If \(\Delta_{\mathrm{r}} G^{\circ}\) for a reaction is negative, the reaction will have an equilibrium constant greater than 1.

Short answer

(a) True, (b) False - exothermic needs \( \Delta G < 0 \), (c) False - high temp may favor products, (d) True - \( K > 1 \).

Step-by-step solution

Analyze Statement (a)

This statement is True. When a substance transitions from liquid to vapor, its molecules obtain more freedom, leading to increased disorder and thus an increase in entropy.

Analyze Statement (b)

This statement is False. An exothermic reaction is not always spontaneous. Spontaneity depends on the Gibbs free energy change: \\[\Delta G = \Delta H - T\Delta S\]A negative \( \Delta G \) indicates spontaneity, which can be affected by both enthalpy and entropy changes. To be spontaneous, the reaction must have a negative \( \Delta G \).

Rewrite Statement (b) to be True

An exothermic reaction will be spontaneous if the change in Gibbs free energy \( \Delta G \) is negative.

Analyze Statement (c)

This statement is False. Reactions with positive \( \Delta_r H^{\circ} \) (endothermic) and positive \( \Delta_r S^{\circ} \) can be spontaneous and product-favored at higher temperatures because entropy increases could outweigh enthalpy changes, leading to a negative \( \Delta G \).

Rewrite Statement (c) to be True

Reactions with a positive \( \Delta_r H^{\circ} \) and a positive \( \Delta_r S^{\circ} \) can be product-favored if the temperature is high enough to make \( \Delta G \) negative.

Analyze Statement (d)

This statement is True. A negative \( \Delta_r G^{\circ} \) means the reaction is spontaneous under standard conditions, which correlates with an equilibrium constant \( K > 1 \), indicating that the products are favored.

Key concepts

Understanding Entropy

Entropy is a measure of disorder or randomness in a system. During a phase transition from liquid to vapor, a substance's molecules gain more movement freedom. As a result, the disorder increases, causing an increase in entropy.
In simpler terms, imagine a group of people. If they are tightly packed together like in a liquid state, their movement is restricted. However, once they spread out into separate spaces like in a vapor state, they have more places to move around. This scenario resembles how molecules behave during the phase transition, leading to increased entropy.
Entropy is crucial for understanding many chemical reactions. Especially in reactions where the number of gas molecules increases, as they are generally associated with increased entropy.

Exploring Enthalpy

Enthalpy refers to the heat content of a system at constant pressure. In chemistry, an exothermic reaction releases heat, indicated by a negative change in enthalpy (\(\Delta H < 0\)). Conversely, an endothermic reaction absorbs heat, leading to a positive enthalpy change (\(\Delta H > 0\)).
Enthalpy alone does not determine whether a reaction is spontaneous. It is one part of the Gibbs Free Energy equation:\[\Delta G = \Delta H - T\Delta S\]where \(T\) is the temperature in Kelvin.
Comprehending enthalpy helps in predicting how reactions behave under different conditions. By examining both enthalpy and entropy, we can better predict the spontaneity of reactions. Understanding these concepts is essential for many scientific fields, including engineering and environmental science.

The Nature of Spontaneous Reactions

In chemical thermodynamics, spontaneous reactions occur naturally without external intervention. However, spontaneity does not solely depend on the reaction releasing energy (exothermic process). Instead, it hinges on the Gibbs Free Energy change (\(\Delta G\)).
A reaction is spontaneous when \(\Delta G\) is negative. This result depends on both the enthalpy (\(\Delta H\)) and the entropy (\(\Delta S\)) changes of a reaction, as described by the equation:\[\Delta G = \Delta H - T\Delta S\]At different temperatures, this equation can lead to changes in spontaneity.
For instance, a reaction with a positive \(\Delta H\) but very positive \(\Delta S\) might be non-spontaneous at low temperatures. Yet, it may become spontaneous at higher temperatures. This versatility makes the concept of spontaneity particularly fascinating and useful for predicting the behavior of chemical reactions.
Spontaneity also helps inform decisions related to chemical manufacturing, energy production, and even biochemistry.

Significance of the Equilibrium Constant

The equilibrium constant (\(K\)) is a vital measure in chemistry that indicates the extent to which a reaction proceeds at equilibrium. When Gibbs Free Energy change (\(\Delta G\)) is negative, it implies that the reaction is spontaneous and product-favored.
This condition leads to an equilibrium constant greater than 1 (\(K > 1\)), showing a significant amount of products over reactants.
This relationship is evident in the equation linking Gibbs Free Energy and the equilibrium constant:\[\Delta G^{\circ} = -RT \ln K\]where \(R\) is the universal gas constant and \(T\) is the temperature in Kelvin.
Understanding the equilibrium constant allows scientists to predict how much of each reactant and product will be present at equilibrium. It also guides chemists in optimizing industrial and laboratory processes by inadvertently indicating reaction favorability and aiding in selecting the best conditions for reactions.