Problem 23 - Chemistry and Chemical Reactivity

Question

Determine whether the reactions listed below are entropy-favored or disfavored under standard conditions. Predict how an increase in temperature will affect the value of \(\Delta_{\mathrm{r}} G^{\circ}.\) (a) \(\mathrm{N}_{2}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g})\) (b) \(2 \mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}(\mathrm{g})\) (c) \(\mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) \rightarrow \mathrm{CaCO}_{3}(\mathrm{s})\) (d) \(2 \mathrm{NaCl}(\mathrm{s}) \rightarrow 2 \mathrm{Na}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{g})\)

Step-by-Step Solution

Answer

Reactions (b) and (d) are entropy-favored. Higher temperature makes entropy-favored reactions more spontaneous and disfavored ones less spontaneous.

Step 1: Calculate Change in Entropy for Each Reaction

To evaluate whether a reaction is entropy-favored, we assess the change in entropy (ΔS) for each reaction. Generally, reactions that produce more gas molecules or greater disorder favor an increase in entropy, while those that decrease the number of gas molecules or produce a more ordered system tend to decrease entropy.

Step 2: Analyze Reaction (a)

In reaction (a) \(\mathrm{N}_{2}( ext{g})+2 \mathrm{O}_{2}( ext{g}) \rightarrow 2 \mathrm{NO}_{2}( ext{g}) \), the reaction starts with three gas molecules and results in two gas molecules. Since the number of molecules decreases, this reaction is entropy-disfavored as it results in a more ordered system.

Step 3: Analyze Reaction (b)

For reaction (b) \(2 \mathrm{C}( ext{s})+\mathrm{O}_{2}( ext{g}) \rightarrow 2 \mathrm{CO}( ext{g}) \), we start with one gas molecule and end with two gas molecules. This increase in the number of gas molecules generally reflects an increase in entropy, making it entropy-favored.

Step 4: Analyze Reaction (c)

In reaction (c) \(\mathrm{CaO}( ext{s})+\mathrm{CO}_{2}( ext{g}) \rightarrow \mathrm{CaCO}_{3}( ext{s}) \), the system begins with one gas and forms a solid product. This transformation from a gas to a solid signifies a decrease in entropy, thus the reaction is entropy-disfavored.

Step 5: Analyze Reaction (d)

For reaction (d) \(2 \mathrm{NaCl}( ext{s}) \rightarrow 2 \mathrm{Na}( ext{s})+\mathrm{Cl}_{2}( ext{g}) \), the reaction produces more disordered products with the creation of chlorine gas from a solid, hence it is entropy-favored due to the increase in disorder.

Step 6: Temperature Effect on Gibbs Free Energy

The reaction's favorability in terms of Gibbs Free Energy (\(\Delta G^\circ\)) is affected by temperature. For reactions that are entropy-favored, increasing temperature will further make the reaction more spontaneous (lower \(\Delta G^\circ\)). Conversely, for entropy-disfavored reactions, increasing temperature will likely make them less spontaneous (higher \(\Delta G^\circ\)).

Key Concepts

Standard Conditions

Standard conditions refer to a set of established baseline conditions under which chemical reactions are analyzed. Generally, these conditions are 25 degrees Celsius (298 K) and 1 atmosphere of pressure. These parameters allow chemists to compare reactions consistently.

Under these standard conditions, measurements of properties like enthalpy ( H extsubscript{f} extsuperscript{0} ), entropy ( S extsubscript{rxn} extsuperscript{0} ), and Gibbs Free Energy ( G extsubscript{rxn} extsuperscript{0} ) are made. By maintaining a common reference point, scientists can predict the feasibility and spontaneity of reactions more accurately.

Think of standard conditions as a "universal language" for chemists, enabling a straightforward comparison of different reactions.

Entropy Change

Entropy change ( ΔS ) refers to the difference in entropy between the products and reactants of a reaction. It's a measure of disorder or randomness in a system. When the number of gas molecules in a reaction increases, the system usually becomes more disordered, leading to a positive ΔS .

In the discussed reactions:

• Reaction (a) shows a decrease in the number of gas molecules, indicating it is entropy-disfavored.
• Reaction (b) increases the number of gas molecules, making it entropy-favored.
• Reaction (c) converts a gas into a solid, showing a decrease in entropy.
• Reaction (d) produces gas from solid, favoring an increase in entropy and disorder.

The concept of entropy helps determine whether a reaction will be spontaneous under specific conditions.

Gibbs Free Energy

Gibbs Free Energy ( ΔG ) is a valuable metric for determining the spontaneity of a chemical reaction. It combines enthalpy ( ΔH ) and entropy ( ΔS ) into one equation: ΔG = ΔH - TΔS .

If ΔG is negative, the reaction is spontaneous under those conditions. Conversely, a positive ΔG indicates a non-spontaneous reaction. This concept is incredibly useful for predicting the likelihood of a chemical process occurring without outside intervention.

In the given reactions, knowing the entropy change helps us understand potential shifts in Gibbs Free Energy, especially as conditions like temperature change.

Temperature Effect

Temperature plays a crucial role in determining the direction and spontaneity of a reaction. A change in temperature modifies the TΔS term in the Gibbs Free Energy equation ( ΔG = ΔH - TΔS ), directly affecting the value of ΔG .

Increasing temperature generally makes reactions that are entropy-favored more spontaneous, lowering ΔG . Conversely, for entropy-disfavored reactions, higher temperatures can make a reaction less spontaneous, increasing ΔG .

Understanding temperature effects is vital for manipulating reaction conditions to favor desired outcomes. It illustrates the dynamic nature of chemical reactions and how they can be influenced by external factors, like heat.