Question

Predict the sign of the entropy change of the system for each of the following reactions: $$\begin{array}{l}{\text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)} \\ {\text { (b) } \mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)} \\ {\text { (c) } 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{6}(g)} \\ {\text { (d) } \mathrm{Al}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Al}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)}\end{array}$$

Short answer

For the given reactions: (a) ΔS is negative due to a decrease in the number of gas particles. (b) ΔS is positive because of the change from solid to gas. (c) ΔS is negative due to a decrease in the number of gas particles. (d) The sign of ΔS for this reaction is difficult to predict without more information.

Step-by-step solution

Reaction (a)

N2(g) + 3 H2(g) → 2 NH3(g) In this reaction, we observe a decrease in the total number of gas particles. Since fewer gas particles are associated with lower entropy, we can expect that the entropy change for this reaction to be negative. So, the entropy change ΔS will be negative.

Reaction (b)

CaCO3(s) → CaO(s) + CO2(g) In this reaction, we see a change in the physical state of one of the reactants (CaCO3) from solid to gas (CO2). When a substance changes to a gaseous state, it tends to increase the entropy of the system. So, the entropy change ΔS will be positive.

Reaction (c)

3 C2H2(g) → C6H6(g) In this reaction, there is a decrease in the total number of gas particles, which is indicative of a decrease in entropy. The entropy change ΔS will be negative for this particular reaction.

Reaction (d)

Al2O3(s) + 3 H2(g) → 2 Al(s) + 3 H2O(g) In this reaction, there is no change in the total number of gas particles, but we observe a transition from a solid (Al2O3) to another solid (Al). However, this change in physical state from one solid to another is unlikely to have a significant effect on the entropy of the system. Therefore, it is difficult to predict the sign of the entropy change for this reaction without more information.

Key concepts

Thermodynamics and Entropy Change

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In thermodynamics, entropy is a crucial concept, representing the degree of disorder or randomness in a system. Entropy change, denoted as \( \Delta S \), is a measure of how much this disorder changes during a process, such as a chemical reaction or a change in physical state.

When we talk about the sign of entropy change, we're looking at whether the disorder in a system increases or decreases. An increase in entropy (\( \Delta S > 0 \) ) is associated with processes where the system becomes more disordered. This often happens when solids melt into liquids, liquids evaporate into gases, or when the number of gaseous molecules increases. On the contrary, a decrease in entropy (\( \Delta S < 0 \) ) occurs when the system becomes more ordered, such as when gases condense into liquids or solids, or when the number of gaseous molecules decreases.

One of the fundamental principles of thermodynamics is the second law, which states that for an isolated system, entropy can never decrease. However, in chemical reactions, we are often dealing with non-isolated systems, where entropy can both increase and decrease, depending on external conditions and the nature of the reactants and products.

Chemical Reactions and Entropy

Chemical reactions involve the breaking and forming of bonds between atoms and the transformation of reactants into products. Entropy plays a key role in these reactions and can help predict the spontaneity of a process. A spontaneous reaction is one that occurs naturally without requiring continuous input of energy from an external source.

Understanding the entropy change in chemical reactions helps us predict whether a reaction is likely to occur. Reactions that result in an increase of gaseous products, or fewer but more complex molecules, typically lead to an increase in entropy. Conversely, reactions that result in fewer gaseous products or a more ordered state will typically have a negative entropy change.

• In reaction (a), the combination of nitrogen and hydrogen gases to form ammonia gas results in fewer gas particles and hence a decrease in entropy.
• Reaction (b), turning solid calcium carbonate into solid calcium oxide and carbon dioxide gas, produces more disorder since a gaseous product is formed, indicating a positive entropy change.
• Reaction (c), converting acetylene gas into benzene gas, decreases the number of molecules and thus leads to lower entropy.

Understanding these changes can guide chemists in predicting the outcome and conditions required for reactions to occur.

Physical States of Matter and Entropy

The physical state of a substance—whether solid, liquid, or gas—affects its entropy. Solids are highly ordered and have the lowest entropy, gases have the highest entropy due to their random motion and high level of disorder, and liquids fall in between.

Changes in physical states are often accompanied by entropy changes:

• A solid melting into a liquid, or a liquid vaporizing into a gas, increases entropy.
• Going from a gas to a liquid or a liquid to a solid would decrease entropy.

In reaction (b), CaCO3 transforming from a solid to a solid and a gas (CO2) increases the entropy due to the production of a gas. However, with reaction (d), while a solid is changing to another solid and a gas, additional details are needed to predict the entropy change, as it's not just the phase change but also the change in molecular complexity and number of particles that determines the overall entropy change.