Question

Explain how an exothermic reaction changes the entropy of the surroundings. Does the enthalpy change for such a reaction increase or decrease \(\Delta G_{\text { system }} ?\) Explain.

Short answer

An exothermic reaction releases heat to the surroundings, causing an increase in the entropy of the surroundings (ΔS_surroundings > 0). The enthalpy change (ΔH) of such a reaction is negative (ΔH < 0). Using the equation \[ΔG = ΔH - TΔS\], we see that a decrease in enthalpy (ΔH) results in a decrease in the Gibbs free energy (ΔG) of the system. Thus, an exothermic reaction increases the entropy of the surroundings and decreases the Gibbs free energy of the system.

Step-by-step solution

Understand the concept of exothermic reaction

Exothermic reactions are chemical reactions that release energy, usually in the form of heat, to the surroundings. This means that exothermic reactions result in a decrease in enthalpy. Mathematically, for an exothermic reaction, ΔH < 0.

Relate heat release and entropy of the surroundings

When heat is released to the surroundings in an exothermic reaction, the temperature of the surroundings increases. As a result, the entropy, which is a measure of the degree of disorder or energy dispersion in a system, also increases. Therefore, for an exothermic reaction, the entropy of the surroundings (ΔS_surroundings) increases (ΔS_surroundings > 0).

Understand the relationship between ΔG, ΔH, and ΔS

To determine how the enthalpy change in an exothermic reaction affects the Gibbs free energy, we must use the equation that relates these three quantities: \[ΔG = ΔH - TΔS\] Here, ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy.

Assess the effect of enthalpy change on ΔG for exothermic reactions

In an exothermic reaction, we know that ΔH < 0 (enthalpy decrease) and ΔS_surroundings > 0 (increase in entropy of the surroundings). From the equation in Step 3, we can see that if ΔH decreases, the overall value of ΔG (i.e., the change in Gibbs free energy) will also decrease. Therefore, the enthalpy change for an exothermic reaction results in a decrease in ΔG. In summary, an exothermic reaction increases the entropy of the surroundings due to the release of heat, and the decrease in enthalpy during the reaction leads to a decrease in the Gibbs free energy (ΔG) of the system.

Key concepts

Enthalpy

Consider enthalpy as a measure of the total energy of a chemical system, often symbolized by \( H \). It encompasses the internal energy, which is the energy required to create the system, and the energy required to make space for it by displacing the environment. In the context of exothermic reactions, where energy is released to the surroundings, enthalpy decreases, denoted by a negative \( \Delta H \) value. This reflects the system losing heat as it provides energy to its surrounding environment.

The concept of enthalpy is central to understanding chemical processes and their energy changes. For example, in our case, when a reaction is exothermic, it can be visualized as the system giving a warm embrace to its surroundings, transferring some of its energy in the form of heat. As a result, this decreases the system's enthalpy because it is essentially losing some of its stored energy. This is like using some of your savings to pay for a communal good, like heating in a shared house; the total 'energy savings' in your personal account go down.

Entropy

Entropy, symbolized by \( S \), is a bit like the measure of randomness or disorder within a system. The more ways the components of the system can be arranged without changing the overall state of the system, the higher the entropy. Think of it like a kid's bedroom: the more scattered the toys, the higher the state of disorder, and hence higher entropy.

An exothermic reaction, which releases energy, tends to increase the temperature of the surroundings. When the surroundings warm up, particles move faster, increasing randomness and the number of possible arrangements—just like when the room heats up and the kid gets more active, flinging toys with even greater abandon. Consequently, the entropy of the surroundings goes up (\(\Delta S_{surroundings} > 0\)), indicating greater disorder. Upon considering this in terms of energy distribution, it means energy is being spread out more widely in the environment, rather than being contained in a structured manner within the reacting chemicals.

Gibbs Free Energy

Gibbs free energy, or \( G \), is the name we give to the energy associated with a chemical reaction that can be used to do work—the 'usable' energy, if you will. It’s a bit like the money left over after you pay your bills that you can use for other things. For a reaction at constant temperature and pressure, the change in Gibbs free energy, \( \Delta G \), determines the spontaneity of the process. A negative \( \Delta G \) means the reaction can occur spontaneously.

The relationship between enthalpy, entropy, and Gibbs free energy is captured beautifully in the equation \[\Delta G = \Delta H - T\Delta S\]. In an exothermic reaction where there is a decrease in enthalpy (\(\Delta H < 0\)) and an increase in entropy of the surroundings (\(\Delta S_{surroundings} > 0\)), the Gibbs free energy typically becomes more negative, indicating a greater 'push' towards spontaneity. This is akin to finding out that not only did your expenses decrease, but also you got a surprise cashback—the unexpected bonus makes it easier to splurge spontaneously on your wants.