Problem 7 - General Chemistry: Principles and Modern Applications

Question

For each of the following reactions, indicate whether \(\Delta S\) for the reaction should be positive or negative. If it is not possible to determine the sign of \(\Delta S\) from the information given, indicate why. (a) \(\mathrm{CaO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\) (b) \(2 \mathrm{HgO}(\mathrm{s}) \longrightarrow 2 \mathrm{Hg}(1)+\mathrm{O}_{2}(\mathrm{g})\) (c) \(2 \mathrm{NaCl}(1) \longrightarrow 2 \mathrm{Na}(1)+\mathrm{Cl}_{2}(\mathrm{g})\) (d) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \longrightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g})\) (e) \(\operatorname{Si}\left(\text { s) }+2 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SiCl}_{4}(\mathrm{g})\right.\)

Step-by-Step Solution

Answer

(a) Not determinable (approximately zero or slightly negative), (b) Positive, (c) Positive, (d) Not determinable (approximately zero or slightly negative or positive), (e) Positive.

Step 1: Analyze reaction (a)

For the reaction \(\mathrm{CaO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\), we can see that the number of molecules in reactant and product side is same (2) and the state of matter doesn't change. Hence, there is no increase in disorder, indicating that \(\Delta S\) for this reaction could be approximately zero or slightly negative.

Step 2: Analyze reaction (b)

For the reaction \(2 \mathrm{HgO}(\mathrm{s}) \longrightarrow 2\mathrm{Hg}(1)+\mathrm{O}_{2}(\mathrm{g})\), the reactants are in solid state and the products include a gas which is more disorderly than a solid. There's an increase in disorder, indicating that \(\Delta S\) for this reaction should be positive.

Step 3: Analyze reaction (c)

For the reaction \(2 \mathrm{NaCl}(1) \longrightarrow 2\mathrm{Na}(1)+\mathrm{Cl}_{2}(\mathrm{g})\), the reactants are in liquid state and the products include a gas. This equates to an increase in disorder, suggesting that the \(\Delta S\) for this reaction should be positive.

Step 4: Analyze reaction (d)

For the reaction \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \longrightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g})\), the overall number of molecules remain same but solid reactant turns to solid product while gas remains gas, the state of matter doesn't change much. Hence, \(\Delta S\) for this reaction could be approximately zero or slightly negative or positive, exact can't be predicted without more data.

Step 5: Analyze reaction (e)

For the reaction \(\operatorname{Si}\left(\text { s) }+2 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SiCl}_{4}(\mathrm{g})\right.\), the reactants include a solid and the product is a gas. There's an increase in disorder, indicating that the \(\Delta S\) for this reaction should be positive.

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances. This transformation occurs through the breaking and forming of chemical bonds. Each reaction can be written as an equation where the substances on the left are the reactants and those on the right are the products.

• States of Matter: In the context of reactions, understanding whether substances are in the solid (s), liquid (l), aqueous (aq), or gas (g) state is crucial, as this affects the reaction process and the properties of the products.
• Reaction Type: Reactions are categorized into different types such as synthesis, decomposition, single replacement, and double replacement. Each type has unique characteristics based on how substances interact and change during the reaction.
• Balancing Reactions: For a reaction to be correctly represented, the number of atoms for each element must be balanced on both sides of the equation, adhering to the Law of Conservation of Mass.

Understanding these aspects helps predict the outcome of reactions, including possible changes in entropy.

Thermodynamics

Thermodynamics is the branch of physics that deals with energy changes, particularly in chemical reactions and physical processes. It helps us understand whether a process will occur spontaneously and how energy is transferred.

• First Law of Thermodynamics: This is the law of energy conservation stating that energy cannot be created or destroyed, only transformed. In reactions, the chemical energy stored in bonds is transformed into heat or work.
• Second Law of Thermodynamics: It states that in any energy transfer, some energy becomes unavailable to do work, typically increasing the disorder or entropy of the system. This principle explains why certain reactions proceed while others do not.
• Gibbs Free Energy: The change in Gibbs Free Energy (\(\Delta G\)) is crucial in determining the spontaneity of reactions. While related to entropy (\(\Delta S\)) and enthalpy (\(\Delta H\)), a negative \(\Delta G\) generally means the reaction can proceed spontaneously.

Understanding these laws provides insight into the energetic feasibility of reactions and their direction.

Disorder in Reactions

Disorder, or entropy (\(\Delta S\)), in chemical reactions is a measure of the randomness or chaos within a system. In the context of chemical reactions, studying how disorder changes helps predict the nature and practicality of reactions.

• Entropy Increase: When reactants transition from an ordered state such as solid (s) to a less ordered state such as gas (g), the disorder typically increases. This is because gas particles move more freely and occupy more volume, leading to higher randomness.


• Entropy Decrease: Conversely, when reactions result in products with less mobility, such as gas to solid transitions, the disorder decreases as particles are more tightly bound.


• Predicting \(\Delta S\): For many reactions, it's possible to qualitatively assess whether \(\Delta S\) is positive or negative based on the states of matter. For example, reactions producing gaseous products usually have a positive \(\Delta S\).

Entropy plays a vital role in assessing whether a reaction is favorable under certain conditions, typically aligning with the laws of thermodynamics.