Determine the standard entropy changes for the following reactions at 25^° C:

(a) H₂ (g) + CuO(s) → Cu(s) + H₂O(g)

(b) 2 Al (s) + 3 ZnO (s) → Al₂O₃ (s) + 3 Zn (s)

(c) CH₄ (g) + 2 O₂ (g) → CO₂ (g) + 2 H₂O (l)

Standard entropy values:

Substance	Standard Entropy (S°) (J/(K·mol))
Cu (s)	33.3
CuO (s)	43.5
H2(g)	131
H2O(g)	188.7
Al(s)	28.33
ZnO(s)	43.9
Zn(s)	41.6
Al2O3(s)	50.99
CH4(g)	186.2
O2(g)	205.0
CO2(g)	213.6
H2O(l)	69.9

Interpretation: The standard entropy changes for a reaction, ∆S°_rxn, is given by the difference in standard entropies between products and reactants. Thus, it reflects the change in disorder or randomness during the reaction.

We can calculate Standard entropy changes by using the following formula:

Where, ∆S^°_rxn = Standard entropy change for the reaction

Solution:

(a) H₂ (g) + CuO(s) → Cu(s) + H₂O(g)

Therefore, the entropy increases by 47.5 J/K.mol for the reaction H₂ (g) + CuO(s) → Cu(s) + H₂O(g)

(b) 2 Al (s) + 3 ZnO (s) → Al₂O₃ (s) + 3 Zn (s)

Therefore, the entropy decreases by – 12.57 J/K.mol for the reaction 2 Al (s) + 3 ZnO (s) → Al₂O₃ (s) + 3 Zn (s).

(c) CH₄ (g) + 2 O₂ (g) → CO₂ (g) + 2 H₂O (l)

Therefore, the entropy increases by 242.8 J/K.mol for the reaction CH₄ (g) + 2 O₂ (g) → CO₂ (g) + 2 H₂O (l).

Determine whether the entropy change is positive or negative for each of the following reactions and explain the reasoning behind your predictions.

1. 2 KClO₄ (s) → 2 KClO₃ (s) + O₂ (g)
2. H₂O (g) → H₂O (l)
3. 2 Na (s) + 2 H₂O (l) → 2 NaOH (aq) + H₂ (g)
4. N₂ (g) → 2 N (g)

Interpretation:

Entropy is a measure of the randomness or disorder within a system. The higher the degree of randomness, the greater the entropy. Among the three primary states of matter, gases possess the highest entropy. The vapor state offers more space for molecules to move compared to the liquid state, and the liquid state provides more freedom of movement than the solid state. Water molecules are ordered more in the solid state than in the liquid or gaseous states. Hence, the entropy order is as follows: S_solid < S_liquid < S_gas .

Here, we aim to determine whether the entropy change is positive or negative in the context of the given reactions. To do this, we will examine the states of the reactants and products involved in the chemical reaction. If the number of gas molecules (∆n_g) increases during the reaction, it results in an increase in entropy, indicating a positive entropy change. Conversely, if the number of gas molecules decreases, the entropy change will be negative.

To calculate this, we will apply the appropriate formula.

Formula

(If ∆n_g is positive, then entropy change will also be positive)

1. 2 KClO₄ (s) → 2 KClO₃ (s) + O₂ (g)

∆n_g is positive, so the entropy change will be positive. Entropy will increase as more and more gas is created.

2. H₂O (g) → H₂O (l)

 ∆n_g is negative, so entropy change will be negative. The formation of liquid will decrease entropy as randomness decreases.

3. 2 Na (s) + 2 H₂O (l) → 2 NaOH (aq) + H₂ (g)

 ∆n_g is positive, so entropy change will be positive. The entropy will increase as more gaseous products are formed.

4. N₂ (g) → 2 N (g)

∆n_g is positive, so the entropy change will be positive. The entropy will increase as more and more gas is created.

How does the entropy of a system change in each of the following processes?

1. Melting of solid
2. Freezing of liquid
3. Boiling of liquid
4. Conversion of vapor to solid
5. Condensation of vapor to liquid
6. Sublimation of solid
7. Dissolution of urea in water

Entropy

In Thermochemistry, entropy is the degree of randomness or disorder in a system. The greater the degree of randomness, the higher the entropy, and vice versa. Entropy describes the spontaneous changes that occur in everyday life or the tendency of the universe towards disorder.

For example, In the morning, when you clean your room and arrange everything neatly, the system has a higher order, however, as you begin your daily activities, especially cooking, things get messy. This is an example of how entropy initially appears lower in an organized state, but as disorder increases and things become more chaotic, the entropy increases.

Entropy is a thermodynamic function that depends on the system’s state rather than the pathway followed. Entropy is an extensive property that scales with the system’s size or extent.

Interpretation

When we increase the temperature, entropy increases. Adding more energy to a system causes the molecules to become more excited, leading to greater randomness. The more random the system, the higher the entropy. Now, let’s determine the change in entropy for the following scenarios:

a. Melting of solid:

In its solid state, ice has molecules fixed in an ordered structure. As it begins to melt, the molecules gain mobility, leading to increased disorder and consequently greater randomness. A higher degree of randomness corresponds to higher entropy. Since the liquid state is more disordered than the solid state, the system’s entropy increases when ice melts.

b. Freezing of liquid

When a liquid freezes, its molecules become more ordered, resulting in a solid with a fixed structure and less randomness. As a result, the degree of disorder decreases. Hence, entropy decreases during the freezing process of liquid.

c. Boiling of liquid

When a liquid begins to boil, the molecules gain more freedom to move independently, which leads to an increase in randomness. The more random a system, the higher its entropy. Since the gaseous state is more random than the liquid state, entropy increases when the liquid turns into gas.

d. Conversion of vapor to a solid

When vapor turns into a solid, the molecules have less freedom to move, causing the level of randomness to decrease. As a result, entropy decreases because the water molecules are more organized in the solid state than the vapor state.

e. Condensation of vapor to liquid

Vapor molecules have more free space to move compared to liquid molecules. Molecules become more organized when the vapor turns into liquid and the randomness decreases. Therefore entropy decreases.

f. Sublimation of solid

When solid sublimes, it is converted to vapor state. As molecules are more ordered in the solid state than the gaseous state, the randomness in the gaseous state is greater, and therefore entropy increases.

g. Dissolution of urea in water

When urea dissolves in water, it forms solid crystals or pellets and is highly soluble. The process of dissolving urea involves transitioning from a more ordered solid state to a less ordered liquid state. As the urea dissolves, the randomness increases, resulting in increased entropy.