Problem 13 - Chemistry: The Central Science

Question

(a) Can endothermic chemical reactions be spontaneous? (b) Can a process that is spontaneous at one temperature be nonspontaneous at a different temperature?

Step-by-Step Solution

Answer

(a) Yes, endothermic chemical reactions can be spontaneous if the increase in entropy (ΔS) and the temperature (T) are high enough to make the Gibbs free energy change (ΔG) negative, such that \(TΔS > ΔH\), where ΔH is the change in enthalpy. (b) Yes, a process that is spontaneous at one temperature can be nonspontaneous at a different temperature due to the influence of temperature on the Gibbs free energy change (\(ΔG = ΔH - TΔS\)). The spontaneity of a reaction depends on the balance between the change in enthalpy (ΔH) and the change in entropy (ΔS), which can be shifted by changes in temperature.

Step 1: Spontaneous endothermic reactions

An endothermic reaction is a reaction in which the system absorbs heat from its surroundings. Spontaneity of a reaction depends on its Gibbs free energy change (\(ΔG\)). If \(ΔG\) is less than zero, the reaction is spontaneous. The Gibbs free energy change is given by the equation: \(ΔG = ΔH - TΔS\) where \(ΔH\) is the change in enthalpy of the reaction, \(T\) is the absolute temperature in Kelvin, and \(ΔS\) is the change in entropy of the reaction. For endothermic reactions, \(ΔH\) is positive as the system is absorbing heat. To make \(ΔG\) negative (a spontaneous reaction), the temperature must be high enough and the increase in entropy (ΔS) of the reaction must be such that \(TΔS\) is greater than \(ΔH\). If \(TΔS > ΔH\), then \(ΔG < 0\) and the endothermic reaction will be spontaneous at that temperature. Therefore, we can conclude that endothermic chemical reactions can be spontaneous if the increase in entropy and the temperature are high enough to make \(ΔG\) negative.

Step 2: Spontaneity at different temperatures

As we have seen in the first part of the solution, the spontaneity of a reaction depends on the Gibbs free energy change, which is influenced by the temperature: \(ΔG = ΔH - TΔS\) This indicates that the spontaneity of a reaction/process can be affected by changes in temperature. A reaction can be spontaneous at one temperature and nonspontaneous at another temperature if the change in temperature shifts the balance between the change in enthalpy (\(ΔH\)) and the change in entropy (\(ΔS\)) so that \(ΔG\) changes from being negative to positive or vice versa. For example, a process that has both a positive \(ΔH\) and a positive \(ΔS\) (e.g., an endothermic reaction, as mentioned earlier) can be spontaneous at high temperatures and nonspontaneous at low temperatures. As the temperature increases, the value of \(TΔS\) increases, so a reaction/process with positive \(ΔS\) will become more likely to have a negative \(ΔG\), making it spontaneous. In conclusion, a process that is spontaneous at one temperature can indeed be nonspontaneous at a different temperature due to the influence of temperature on the Gibbs free energy change.

Key Concepts

Endothermic Reactions

Endothermic reactions are fascinating because they absorb heat from their surroundings. This means that as these reactions occur, they are taking in energy rather than releasing it. But one might wonder: can such a process ever happen spontaneously? The answer lies in the concept of Gibbs free energy, which is the key factor in determining the spontaneity of a chemical reaction.
To determine if an endothermic reaction can be spontaneous, we look at the equation for Gibbs free energy change, \( ΔG = ΔH - TΔS \). Here, \( ΔH \) represents the change in enthalpy, \( T \) is the temperature in Kelvin, and \( ΔS \) is the change in entropy. While \( ΔH \) is positive for endothermic reactions (indicating heat absorption), the crucial part is whether the entropy change \( (ΔS) \) and the temperature are high enough to drive \( ΔG \) to be negative.
In simpler terms:

• An endothermic reaction is spontaneous if the entropy increase (\(ΔS\)) and temperature (\(T\)) make the term \(TΔS\) larger than \(ΔH\).
• When \( TΔS > ΔH \), the reaction has a negative \( ΔG \), indicating spontaneity despite being endothermic.

Spontaneous Reactions

Spontaneous reactions occur without external input, driven by the system's natural tendency to become more disordered or more stable. Gibbs free energy change \( (ΔG) \) is the deciding factor for spontaneity. When \(ΔG\) is negative, a reaction occurs spontaneously.
It's essential to realize that spontaneity is not synonymous with speed. A reaction can be spontaneous but still occur very slowly due to kinetic factors.
In the context of endothermic reactions, even when energy is absorbed, the increase in disorder (entropy) can be so significant that it results in a process that occurs spontaneously, as long as \(TΔS\) can overcome \(ΔH\). The concept of spontaneity showcases the intricate balance between energy, entropy, and temperature.

• Negative \(ΔG\) indicates spontaneity.
• Spontaneity does not correlate with the reaction rate.
• Endothermic reactions can be spontaneous with sufficient entropy gain.

Temperature Dependency of Reactions

Temperature plays a crucial role in determining whether a reaction is spontaneous or not. The equation \( ΔG = ΔH - TΔS \) clearly shows the temperature's impact on a reaction's spontaneity.
For many reactions, changing the temperature can switch a process from being spontaneous to nonspontaneous or vice versa. Consider a reaction with a positive \( ΔH \) and \( ΔS \). At lower temperatures, \( ΔH \) can dominate, rendering them nonspontaneous. But as the temperature rises, \( TΔS \) increases and can surpass \( ΔH \), making \( ΔG \) negative, hence the reaction becomes spontaneous.
This dependency is why certain processes, like melting ice, only occur or reverse under specific temperature conditions.

• Higher temperatures may favor spontaneous reactions with positive \(ΔS\).
• A reaction's spontaneity can change with temperature shifts.
• Understanding temperature effects helps predict reaction behavior under different conditions.