Understanding Entropy Change in the Formation of CO2 from Carbon and Oxygen

Entropy change, denoted as ΔS, is a critical concept in thermodynamics, especially when evaluating the spontaneity and direction of chemical reactions. This article delves into the entropy change associated with the formation of 1 mole of carbon dioxide (CO2) from 1 mole of solid carbon graphite and 1 mole of oxygen gas (O2). Understanding this process is essential for comprehending the thermodynamics behind this reaction.

Entropy Change Calculation for the Reaction

The reaction of interest is the formation of CO2 from carbon and oxygen gas:

C(s) O2(g) rarr; CO2(g)

Initial and Final States

In the context of entropy, we need to consider both the number of moles of gaseous and solid species involved in the reaction and their respective states. Let's break down the initial and final states:

Initial State

- 1 mole of C(s) (solid carbon graphite): This has a lower entropy compared to gaseous species.

- 1 mole of O2(g) (gaseous oxygen): This has a higher entropy.

Final State

- 1 mole of CO2(g) (gaseous carbon dioxide): This also has a higher entropy than the solid reactants.

Entropy Contribution Analysis

When 1 mole of solid carbon reacts with 1 mole of gaseous oxygen, the entropy change can be analyzed as follows:

Solid Carbon to Gaseous CO2: The transition from the solid state to the gaseous state of carbon (via the formation of CO2) involves a significant increase in entropy. This is because gases have much higher entropy compared to solids. Gaseous O2: The gaseous form of oxygen contributes to the overall entropy. Total Entropy: The final state consists of 1 mole of gaseous CO2, which is at a higher entropy level than the initial state.

Conclusion and Overall Entropy Change

Although one might intuitively think that the reaction decreases the number of gas moles from 1 mole of O2 to 1 mole of CO2, the overall entropy change is influenced by the states of the reactants and products. Here#39;s why:

Conversion of Solid to Gas: The conversion of solid carbon to gaseous CO2 significantly increases the entropy of the system. Gaseous Reactant: The presence of gaseous oxygen further contributes to the entropy increase. Overall Entropy Increase: The reaction ultimately leads to an increase in the entropy of the system, as the formation of 1 mole of CO2 (a gaseous product) from the given reactants results in a higher overall entropy state.

Therefore, the entropy change (ΔS) for this reaction is positive, indicating an increase in the disorder or randomness of the system. This aligns with the general principle that reactions producing gases from solids or liquids typically lead to an increase in entropy.

Quantitative Calculation of Entropy Change

To determine the exact entropy change (ΔS) during this reaction, one needs to look up the standard entropies of the reactants and products in a thermodynamic table. The standard entropies of these species can then be used to calculate the entropy change for the reaction. Another approach includes using the relationship between enthalpy, Gibbs free energy, and temperature:

ΔS (ΔG - ΔH)/T

Where:

ΔG - standard Gibbs free energy change ΔH - standard enthalpy change T - temperature in Kelvin

By obtaining these values, one can accurately determine the entropy change for the reaction. Additionally, since the reaction is highly irreversible, the end products will predominantly be in the form of either 0 moles or 1 mole of each species at equilibrium.