Question

Express the increase of entropy principle for chemically reacting systems.

Short answer

Answer: The two main components affecting the entropy change in a chemically reacting system are (1) entropy changes due to the heat and work interactions between the system and its surroundings (i.e., thermodynamic entropy change) and (2) entropy changes due to the reaction itself (i.e., reaction entropy). The total entropy change of an isolated chemically reacting system can be expressed according to the increase of entropy principle as: ∆S_total (isolated system) = ∆S_thermodynamic + ∆S_reaction ≥ 0

Step-by-step solution

Understand the entropy change in a chemically reacting system

In a chemically reacting system, there are two main components affecting the entropy change: (1) entropy changes due to the heat and work interactions between the system and its surroundings (i.e., thermodynamic entropy change) and (2) entropy changes due to the reaction itself (i.e., reaction entropy). The total entropy change of the system ∆S is the sum of these two components: ∆S_total = ∆S_thermodynamic + ∆S_reaction.

Define the thermodynamic entropy change

The thermodynamic entropy change (∆S_thermodynamic) of a system can be calculated using the formula: ∆S_thermodynamic = ∫(dQ/T) where dQ is the differential amount of heat absorbed by the system and T is the absolute temperature. We have to calculate this integral over the process path for a given system.

Define the reaction entropy

The reaction entropy (∆S_reaction) is the difference in entropy between the products and reactants in a chemical reaction. It can be calculated as: ∆S_reaction = Σν_i * S_i(products) - Σν_i * S_i(reactants) where ν_i is the stoichiometric coefficient of species i, S_i(products) is the entropy of species i in the product, and S_i(reactants) is the entropy of species i in the reactant. The terms need to be summed up for all the species involved in the reaction.

Apply the increase of entropy principle to chemically reacting systems

For an isolated chemically reacting system, the increase of entropy principle states that the total entropy change must be greater than or equal to zero: ∆S_total (isolated system) = ∆S_thermodynamic + ∆S_reaction ≥ 0 This expression is the increase of entropy principle applied to chemically reacting systems, and it helps to analyze various chemical processes, including equilibrium and non-equilibrium conditions of the system.

Key concepts

Thermodynamic Entropy Change

When we discuss thermodynamic entropy change in the context of chemically reacting systems, we're referring to the change in disorder or randomness within a system due to heat and work interactions with the surroundings. Entropy, as a fundamental thermodynamic property, measures the number of microscopic configurations that correspond to a thermodynamically macroscopic state.

The formula \(\Delta S_{thermodynamic} = \int(\frac{dQ}{T})\) quantifies this change, integrating the small amount of heat \(dQ\), at a given absolute temperature \(T\), over a system's process path. What's crucial to realize is that this formula assumes the process is reversible and the temperature is constant, hence the need to perform the integral along the specific path of the process.

In the context of an educational platform, we emphasize the visualization of this concept by picturing a graph of temperature versus entropy and imagining the area under the curve as representing the thermodynamic entropy change. This concept is integral in understanding how energy flows and disperses within a system, which is vital for a student trying to grasp complex topics in thermodynamics and chemical reactions.

Reaction Entropy

The term reaction entropy, denoted as \(\Delta S_{reaction}\), specifically refers to the change in entropy as a result of a chemical reaction taking place. This change reflects the degree of disorder arising from the transformation of reactants into products. It's calculated by the formula
\(\Delta S_{reaction} = \Sigma u_i \cdot S_i(\text{products}) - \Sigma u_i \cdot S_i(\text{reactants})\),
where \(u_i\) represents the stoichiometric coefficient, and \(S_i\) denotes the entropy of a specific species, either in the product mix or the reactant mix. Learning to use this equation helps students to predict the direction of a chemical reaction and to understand how the molecular structure and quantity influence the disorder of the system.

Importantly, reaction entropy can help indicate whether a reaction will proceed spontaneously. A positive value of \(\Delta S_{reaction}\) suggests that the reaction may be spontaneous under certain conditions, as it leads to an increase in randomness. Students should note, however, that spontaneity also depends on other factors, such as the change in enthalpy and temperature of the reaction.

Isolated Chemically Reacting Systems

Isolated chemically reacting systems are ones that do not exchange matter or energy with their surroundings. In such systems, the entropy can only stay the same or increase, as stated by the second law of thermodynamics. This is important because it places a fundamental constraint on the direction of chemical reactions and processes.

The expression \(\Delta S_{total} (isolated system) = \Delta S_{thermodynamic} + \Delta S_{reaction} \geq 0\) exemplifies the principle of entropy increase for chemically reacting systems in isolation. It tells us that the universe's total entropy, including our system and its surroundings, should either remain unchanged or increase after a process occurs.

Students should understand that in real-world applications, perfectly isolated systems are an idealization. Nevertheless, using this concept is essential in predicting the feasibility of chemical reactions, and it plays a crucial role in areas such as chemical engineering, environmental science, and even cosmology, where the understanding of isolated system behavior is pivotal.