Problem 28 - Chemistry The Molecular Science

Question

Without doing a calculation, predict whether the entropy change is positive or negative when each reaction occurs in the direction it is written. (a) \(\mathrm{CH}_{3} \mathrm{OH}(\ell) \longrightarrow \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g})\) (b) \(\mathrm{Br}_{2}(\ell)+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HBr}(\mathrm{g})\) (c) \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{CH}_{4}(\mathrm{~g})\) (d) \(\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{I}^{-}(\mathrm{aq}) \longrightarrow \mathrm{AgI}(\mathrm{s})\)

Step-by-Step Solution

Answer

(a) Positive, (b) Positive, (c) Positive, (d) Negative.

Step 1: Analyze Reaction (a)

In the reaction \( \mathrm{CH}_3\mathrm{OH}(\ell) \rightarrow \mathrm{CO}(\mathrm{g}) + 2 \mathrm{H}_2(\mathrm{g}) \), a liquid is converted into gases. Gases have higher entropy than liquids due to their greater freedom of movement. The number of moles is also increasing from 1 to 3. Thus, the entropy change \( \Delta S \) is positive.

Step 2: Analyze Reaction (b)

For the reaction \( \mathrm{Br}_2(\ell) + \mathrm{H}_2(\mathrm{g}) \rightarrow 2 \mathrm{HBr}(\mathrm{g}) \), a liquid and a gas combine to form two moles of gas. Entropy changes are better understood by comparing moles of gas: 1 mole of gas is converted into 2 moles. Consequently, \( \Delta S \) is expected to be positive because gas production increases disorder.

Step 3: Analyze Reaction (c)

In this reaction \( \mathrm{C}_3\mathrm{H}_8(\mathrm{g}) \rightarrow \mathrm{C}_2\mathrm{H}_4(\mathrm{g}) + \mathrm{CH}_4(\mathrm{g}) \), 1 mole of gas is split into 2 moles of gas. Since gas phase entropy is largely dependent on the number of moles, \( \Delta S \) should be positive as the total moles of gas increase.

Step 4: Analyze Reaction (d)

In the reaction \( \mathrm{Ag}^+(\mathrm{aq}) + \mathrm{I}^-(\mathrm{aq}) \rightarrow \mathrm{AgI}(\mathrm{s}) \), ions in an aqueous solution form a solid. Liquids and solutions generally have higher entropy than solids because solids have more ordered structures. Thus, \( \Delta S \) is negative as it transitions to a less random state.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy is a crucial concept in thermodynamics that helps us predict whether a reaction will happen spontaneously. The formula for Gibbs Free Energy (G) is \( \Delta G = \Delta H - T\Delta S \), where \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.
This formula links these three quantities to evaluate the feasibility of a chemical reaction.

• If \( \Delta G \)< 0, the reaction happens spontaneously.
• If \( \Delta G \)> 0, the reaction is non-spontaneous.
• If \( \Delta G \)= 0, the system is at equilibrium.

Despite analyzing Gibbs Free Energy, entropy plays a significant role in determining spontaneity. In reactions that increase the entropy (\( \Delta S > 0 \)), the system tends to become more disordered, favoring spontaneity at higher temperatures. Thus, Gibbs Free Energy offers a comprehensive framework to explore the balance between energy and disorder in reactions.

Reaction Prediction

Predicting the direction of a chemical reaction without extensive calculations involves understanding several factors. One of these factors is the entropy change (\( \Delta S \)) associated with the reaction.
In the original exercise, the change in entropy informed the prediction of whether the reactions are spontaneous or not.
The key observations include:

• Reactions that produce more gas molecules, such as in reactions (a) and (b), often have a positive \( \Delta S \) because gases have higher entropy than liquids or solids due to higher disorder.
• In contrast, reactions moving towards solid formation, like in reaction (d), show a negative \( \Delta S \) as the system becomes more ordered.

These insights allow chemists to hypothesize the spontaneity of reactions by simply observing states of matter and counting moles, thereby applying simple thermodynamic principles without direct calculation.

Thermodynamics in Chemistry

Thermodynamics in chemistry encapsulates concepts such as energy changes and the behavior of substances in reaction processes. It helps us comprehend why certain reactions occur while others do not. It focuses on the interplay between the energy and disorder within a system.
Entropy, the measure of disorder or randomness, is one of the pillars of thermodynamics. It plays a large role in reaction dynamics. In the exercise, for instance, changes in entropy provide insights into how reactions evolve towards more or less disorder.
Thermodynamics relies on several laws governing energy transformations:

• The First Law, or the law of energy conservation, states that energy cannot be created or destroyed. This greatly affects how energy changes, such as enthalpy, are balanced in reactions.
• The Second Law addresses the inevitability of disorder, highlighting that in any spontaneous process, the total entropy of a system and its surroundings always increases.

By applying these principles, scientists can predict the course and equilibrium position of chemical reactions. Thus, understanding these thermodynamic laws is vital for tapping into the behavior and tendencies of matter during chemical processes.