Problem 89 - Chemistry The Central Science In Si Units

Question

The reaction \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\) is highly spontaneous. A classmate calculates the entropy change for this reaction and obtains a large negative value for \(\Delta S^{\circ} .\) Did your classmate make a mistake in the calculation? Explain.

Step-by-Step Solution

Answer

No, the classmate did not make a mistake; the calculation likely reflects the phase transition from gas to solid.

Step 1: Understand the Reaction

The reaction involves two moles of magnesium (\(\mathrm{Mg}(s)\)) reacting with one mole of oxygen gas (\(\mathrm{O}_{2}(g)\)) to produce two moles of magnesium oxide (\(\mathrm{MgO}(s)\)). This is a combustion reaction.

Step 2: Evaluate Phases of Reactants and Products

Evaluate the phases: The reactants include one gaseous molecule, \(\mathrm{O}_{2}(g)\), and the products are solid, \(\mathrm{MgO}(s)\). Transitioning from a gaseous state to a solid state typically results in a decrease in entropy.

Step 3: Analyze Entropy Change (\(\Delta S^{\circ}\))

Entropy (\(S\)) tends to decrease when gases are converted into solids. In this reaction, since a gas is used up and solid is formed, the change in entropy, \(\Delta S^{\circ}\), is expected to be negative. Thus, obtaining a large negative value for \(\Delta S^{\circ}\) is consistent with the transition from gas to solid described here.

Step 4: Determine if a Mistake Was Made

Since the transition from a less ordered phase (gas) to a more ordered phase (solid) typically results in a negative \(\Delta S^{\circ}\), and the process is spontaneous but with unfavorable entropy, your classmate's calculation is likely correct and not indicative of a mistake regarding this aspect.

Key Concepts

Spontaneous Reaction

In thermodynamics, a spontaneous reaction is one that occurs naturally under specific conditions without external influence. This does not necessarily mean it happens quickly, but rather it is thermodynamically favored. Spontaneity depends largely on two primary factors:

• Changes in enthalpy (H)
• Changes in entropy (S)

A reaction is typically spontaneous if it results in a decrease in the system's free energy, denoted by the Gibbs free energy change (G). For a spontaneous process, G is negative. In this equation: \[delta G = H - TS\]the temperature (T) and the balance between enthalpy and entropy changes determine spontaneity. Even if the entropy change (S) is negative, as seen in exothermic combustion reactions, the reaction can still be spontaneous if the enthalpy change (H) more than compensates, resulting in a negative G.

Combustion Reaction

A combustion reaction involves the burning of a substance in the presence of oxygen. It results in the release of energy in the form of heat or light. Combustion reactions are typically exothermic, meaning they release energy, which contributes to their spontaneity.
In the exercise given, the combustion reaction of magnesium with oxygen forms magnesium oxide. Initially, magnesium and oxygen are in free and reactive states:

• Magnesium solid (Mg(s)
• Oxygen gas (O_2(g)

This reaction rapidly produces:

• Magnesium oxide solid (MgO(s)

The overall reaction displays an organized transfer of reactants into a more stable product while releasing a significant amount of energy. This energy release is a key indicator of many combustion reactions.

Phase Transition

Phase transition refers to the transformation of a substance from one state of matter to another, such as solid to liquid, liquid to gas, or, as in this exercise, gas to solid. The combustion reaction of magnesium involves a phase transition of oxygen gas to magnesium oxide solid.
This kind of transition is characterized by a change in entropy (S), which signifies the degree of disorder. Going from a gaseous state, which is more disordered, to a solid, which is more ordered, results in a decrease in entropy.

• A gas has more randomness - High entropy
• A solid has organized structures - Low entropy

In thermodynamic terms, this transition is significant because it affects the entropy component of the Gibbs free energy equation, thereby influencing the spontaneity of the reaction.

Thermodynamics

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. It provides a comprehensive framework to understand processes such as chemical reactions, especially in terms of energy changes and conservation. In the exercise, thermodynamics helps explain the spontaneous nature of the magnesium combustion reaction by looking at:

• Enthalpy change (H)
• Entropy change (S)
• Temperature at which the reaction occurs

These factors are quantitatively related through the Gibbs free energy change (G) to determine reaction spontaneity. Thermodynamics also encapsulates laws that dictate energy conservation and conversion, thus ensuring that during any reaction, the total energy remains constant. Understanding this helps one predict how and why reactions occur under specific conditions, beyond mere experimental observations. This comprehension is crucial for analyzing real-life chemical reactions in depth.