Question

Predict the sign of \(\Delta S^{\circ}\) for each of the following reactions. (a) \(\mathrm{CCl}_{4}(l)+5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{ClO}_{2}(g)\) (b) \(8 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{S}_{8}(s) \longrightarrow 8 \mathrm{H}_{2} \mathrm{~S}(g)+4 \mathrm{O}_{2}(g)\) (c) \(\mathrm{Br}_{2}(l) \longrightarrow \mathrm{Br}_{2}(s)\) (d) \(2 \mathrm{NH}_{3}(\mathrm{~g}) \longrightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)\)

Short answer

Question: Predict the sign of ΔS° (standard entropy change) for each of the following reactions. (a) CCl4(l) + 5 O2(g) → CO2(g) + 4 ClO2(g) (b) 8 H2O(l) + S8(s) → 8 H2S(g) + 4 O2(g) (c) Br2(l) → Br2(s) (d) 2 NH3(g) → N2(g) + 3 H2(g) Answer: (a) ΔS° is positive. (b) ΔS° is positive. (c) ΔS° is negative. (d) ΔS° is positive.

Step-by-step solution

Reaction (a)

For the reaction: \(\mathrm{CCl}_{4}(l)+5 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+4 \mathrm{ClO}_{2}(g)\). In this reaction, there is an increase in the number of moles of gas from 5 to 5+4=9, meaning there's an increase in the disorder of the system. As a result, the sign of ΔS° will be positive.

Reaction (b)

For the reaction: \(8 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{S}_{8}(s) \longrightarrow 8 \mathrm{H}_{2} \mathrm{S}(g)+4 \mathrm{O}_{2}(g)\). In this reaction, there is an increase in the number of moles of gas from 0 to 8+4=12, meaning there's an increase in the disorder of the system. Moreover, there's a change in the physical state of water from liquid to gas. Thus, the sign of ΔS° will be positive.

Reaction (c)

For the reaction: \(\mathrm{Br}_{2}(l) \longrightarrow \mathrm{Br}_{2}(s)\). In this reaction, there is a change in the physical state of bromine from liquid to solid, which reduces the disorder of the system. Consequently, the sign of ΔS° will be negative.

Reaction (d)

For the reaction: \(2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{N}_{2}(g)+3\mathrm{H}_{2}(g)\). In this reaction, there is an increase in the number of moles of gas from 2 to 1+3=4, meaning there's an increase in the disorder of the system. Therefore, the sign of ΔS° will be positive.

Key concepts

Entropy (ΔS°)

Entropy is a thermodynamic property that measures the level of disorder or randomness in a system. Think of it like how messy your room can get — the messier it is, the higher its 'entropy'. In chemical reactions, entropy can change as products and reactants shift from one physical state to another or as the number of particles in the system changes.

When predicting the sign of tropy change (ΔS°), a positive sign (+) signifies an increase in disorder, much like clothes scattered across your room. Conversely, a negative sign (−) indicates a reduction in chaos, akin to tidying up. In chemical equations, when gaseous substances are produced from liquids or solids, the gas particles can move more freely, thus increasing entropy. For instance, if a solid melts into a liquid, the movement of particles is less restricted, so tropy increases—this is reflected in a positive ΔS°.

Physical State Changes

Transitions between various physical states—such as solids, liquids, and gases—play a critical role in the change of entropy during chemical reactions. Each state has a distinct level of disorder: solids are well-ordered, liquids are less so, and gases are the most chaotic.

Melting, Boiling, and Freezing

When a solid melts or a liquid boils, the particles gain freedom of movement, leading to higher entropy. In contrast, when gas condenses or liquid freezes, particles become more confined, lowering the system's entropy. For example, when bromine transitions from a liquid to a solid, it's akin to moving from a state of wandering freely around your home to just sitting on your sofa; there's less freedom, hence lower entropy, symbolized by a negative ΔS°.

Mole Concept in Gases

In chemistry, the mole is a unit that allows us to count atoms, molecules, or ions in bulk. The idea is similar to a dozen eggs being a way to easily count eggs. For gases, which are composed of free-moving particles that fill their container, the number of moles can give us a clear idea about a substance's quantity.

Volume and Number of Particles

One mole of any gas at standard temperature and pressure occupies the same volume — about 22.4 liters. So, when we look at chemical reactions involving gases, we can predict changes in entropy by comparing the moles of gases before and after the reaction. If more moles of gas are produced, as in the equation where ammonia (NH3) breaks down into nitrogen (N2) and hydrogen (H2), we have more particles occupying a greater volume, thus a positive ΔS°.

Spontaneity of Reactions

Spontaneity in chemistry refers to whether a reaction will occur without needing an external force or energy. Not every reaction that's spontaneous is rapid; some can be quite slow, like the rusting of iron. Entropy is a major player in determining spontaneity through the second law of thermodynamics, which states that for a process to be spontaneous, the total entropy of the system and its surroundings must increase.

Gibbs Free Energy

To predict the spontaneity of a reaction, scientists often use Gibbs free energy, a measure that combines entropy and another thermodynamic property, enthalpy. A negative Gibbs free energy indicates a spontaneous reaction. While increasing entropy usually suggests spontaneity, it's the delicate balance between entropy and enthalpy that ultimately decides a reaction's fate. If a change leads to significantly higher disorder (higher ΔS°) and sufficient enthalpic favorability, spontaneity is likely.