Question

\(\Delta S^{\circ}\) will be highest for the rcaction (1) Ca(s) \(11 / 2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CaO}(\mathrm{s})\) (2) \(\mathrm{CaCO}_{3}(\mathrm{~s}) \longrightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{~g})\) (3) C(s) \(1 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})\) (4) \(\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})\)

Short answer

Reaction (2) CaCO3(s) → CaO(s) + CO2(g) has the highest ΔS°.

Step-by-step solution

- Identify the change in state

Consider the states of reactants and products in each reaction. (1) Ca(s) + 1/2 O2(g) → CaO(s): A solid and gas react to form a solid.(2) CaCO3(s) → CaO(s) + CO2(g): A solid decomposes into a solid and a gas.(3) C(s) + O2(g) → CO2(g): A solid and gas react to form a gas.(4) N2(g) + O2(g) → 2 NO(g): Two gases react to form another gas.

- Determine the change in entropy (ΔS)

Entropy tends to increase when a solid or liquid changes to a gas, and decrease when a gas changes to a solid or liquid. Compare the change in the number of gas molecules in each reaction:(1) Gas molecules decrease.(2) Gas molecules increase (one gas molecule CO2 is produced).(3) No change in the number of gas molecules (one gas molecule O2 reacts to form one gas molecule CO2).(4) No significant change (one O2 and one N2 form two NO gases).

- Identify the reaction with the highest increase in entropy

The reaction that shows the highest increase in the number of gas molecules will have the highest ΔS°. Here, reaction (2) is the only one where a solid decomposes to produce a gas, leading to a significant increase in entropy.

Key concepts

Change in Entropy

Entropy, represented as ΔS, measures the disorder or randomness in a system. A change in entropy occurs during chemical reactions when the state or number of molecules changes.

For example, when a solid turns into a gas, the entropy increases because gas molecules have more freedom to move around. Conversely, when a gas turns into a solid, the entropy decreases.

In our given reactions, we need to consider how the states of matter and the number of gas molecules change to determine the change in entropy. The reaction with the highest increase in the number of gas molecules will have the highest ΔS°. This is because gases have higher entropy compared to solids and liquids.

States of Matter in Reactions

The state of matter—whether something is a solid, liquid, or gas—affects entropy.

Let's break down the given reactions:

• Reaction 1: Ca(s) + 1/2 O2(g) → CaO(s) - We have a solid and a gas forming a solid.
• Reaction 2: CaCO3(s) → CaO(s) + CO2(g) - A solid decomposes into a solid and a gas.
• Reaction 3: C(s) + O2(g) → CO2(g) - A solid and a gas forming a gas.
• Reaction 4: N2(g) + O2(g) → 2 NO(g) - Two gases react to form another gas.

By analyzing the above, we can see that reactions involving gases generally lead to higher entropy, while reactions that form solids from gases may lead to lower entropy.

Gas Molecule Production

The production of gas molecules is a key factor in determining the change in entropy.

Reactions that produce more gas molecules than they consume will generally increase entropy. In our list of reactions:

• Reaction 1: The number of gas molecules decreases.
• Reaction 2: One gas molecule (CO2) is produced from a solid (CaCO3).
• Reaction 3: The number of gas molecules remains the same.
• Reaction 4: The number of gas molecules remains roughly the same (two gases form two other gas molecules).

Therefore, Reaction 2 has a notable increase in the number of gas molecules, leading to an increase in entropy.

Chemical Reaction Analysis

To fully analyze the chemical reactions, we need to look at both the change in states of matter and the number of gas molecules involved.

Considering all reactions:
ineach step:

• Reaction 1: A solid and a gas react to form a solid, leading to a decrease in entropy.
• Reaction 2: A solid decomposes into a solid and a gas, leading to an increase in entropy.
• Reaction 3: A solid and a gas react to form a gas, leading to no significant change in entropy.
• Reaction 4: Two gases react to form another gas, leading to no significant change in entropy.

Based on this analysis, the reaction with the highest increase in entropy is Reaction 2 (CaCO3 decomposing into CaO and CO2), as it involves a solid turning into a gas.