Question

Predict whether the entropy change is positive or negative for each of the following reactions. Give reasons for your predictions. (a) \(2 \mathrm{KClO}_{4}(s) \longrightarrow 2 \mathrm{KClO}_{3}(s)+\mathrm{O}_{2}(g)\) (b) \(\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)\) (d) \(\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{~N}(g)\)

Short answer

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

Step-by-step solution

Analyze Reaction (a)

The reaction is \( 2 \text{KClO}_4(s) \rightarrow 2 \text{KClO}_3(s) + \text{O}_2(g) \). Initially, both reactants are solids, and the products include a gas. The formation of a gas increases the disorder or randomness of the system. This suggests an increase in entropy. Thus, the change in entropy is positive.

Analyze Reaction (b)

For the reaction \( \text{H}_2\text{O}(g) \rightarrow \text{H}_2\text{O}(l) \), the substance goes from a gaseous state to a liquid state. Gases have more disorder compared to liquids. Therefore, the transition to a liquid corresponds to a decrease in entropy. The entropy change is negative.

Analyze Reaction (c)

The reaction \( 2 \text{Na}(s) + 2 \text{H}_2\text{O}(l) \rightarrow 2 \text{NaOH}(aq) + \text{H}_2(g) \) involves solids and liquids initially, resulting in an aqueous solution and a gas. The formation of a gas from a solid and liquid typically increases entropy due to the increase in disorder. Hence, the entropy change is positive.

Analyze Reaction (d)

In the reaction \( \text{N}_2(g) \rightarrow 2 \text{N}(g) \), a single gaseous molecule is splitting into two separate gaseous atoms. This increases the disorder or randomness of the system because there are more ways to distribute energy among the separated atoms. Thus, the entropy change is positive.

Key concepts

Predicting Entropy

When predicting entropy change in a chemical reaction, think of it as a measure of disorder or randomness. Entropy, represented by the symbol \( S \), often increases when the arrangement of particles becomes less ordered. Let's break it down:

• Entropy tends to increase with more distributed particles, such as going from solid to liquid or liquid to gas.
• Entropy usually decreases when systems become more ordered, like gas condensing into a liquid.

In reactions, asking whether the system tends towards more disorder helps predict if entropy increases or decreases. It's like messy versus tidy rooms; messier means higher entropy!

States of Matter

The state of matter plays a crucial role in determining entropy. Matter can exist in different states: solid, liquid, and gas. Each has unique properties that influence entropy:

• Solids: Particles are closely packed, limiting their movement. This means low entropy due to ordered structure.
• Liquids: Particles have more freedom to move compared to solids, leading to moderate entropy.
• Gases: Particles move freely and independently, resulting in high entropy due to random structure.

For example, heating can change these states, typically increasing entropy when moving to a higher energy state like gas.

Reaction Analysis

Analyzing a reaction helps determine if entropy increases or decreases. Look at how substances change state and configuration:

• Identify if gases are formed or consumed.
• Notice changes in the number of molecules.

Reaction (a) shows the decomposition of a solid into a gas, suggesting an increase in entropy due to the formation of additional particles and states.

In reaction (b), water condenses from gas to liquid, reducing entropy because of the transition to a more ordered state. Understanding the type of matter and how it changes are essential to predicting entropy for any chemical reaction.

Entropy Increase

Entropy increases when a system becomes more disordered, often observable during particular chemical reactions:

• Supplement of gaseous products enhances entropy, as observed in reactions (a) and (c) where gases are generated.
• Increasing the number of particles in the product side, like in reaction (d), disrupts previous order and increases randomness.

Overall, any transformation that increases the range of motion and distribution of particles generally leads to higher entropy levels. Reactions that produce gas or significantly rearrange atoms often result in such increases.

Entropy Decrease

When entropy decreases, the system transitions into a more ordered state. This typically happens in scenarios such as:

• Formation of a liquid or solid from a gas, as seen in reaction (b), water transitions from a gas to liquid.
• Reduced number of moles of gaseous products or reactants.

In such processes, the entropy decreases because the energy distribution among particles becomes more constrained, leading to greater order.