Question

On the basis of your experience, predict which reactions are spontaneous: (a) \(\mathrm{PbO}_{2}(s) \longrightarrow \mathrm{Pb}(s)+\mathrm{O}_{2}(g)\) (b) \(\mathrm{N}_{2}(l) \longrightarrow \mathrm{N}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) (c) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(l)\) at \(25^{\circ} \mathrm{C}\) (d) \(\mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{3}^{2-}(a q) \longrightarrow \mathrm{CaCO}_{3}(s)\)

Short answer

(a) PbO2(s) → Pb(s) + O2(g) (b) N2(l) → N2(g) at 25°C (c) C6H12O6(s) → C6H12O6(l) at 25°C (d) Ca²⁺(aq) + CO3²⁻(aq) → CaCO3(s) Answer: Reactions (b) and (d) are spontaneous.

Step-by-step solution

Reaction (a): PbO2(s) → Pb(s) + O2(g)

For this reaction, the product contains a gas molecule while the reactant does not. Generally, forming gas molecules increases the entropy of the system, which would make the reaction favorable. However, this reaction involves the reduction of lead oxide to lead, which is not favorable without an external energy source. Therefore, this reaction is not spontaneous.

Reaction (b): N2(l) → N2(g) at 25°C

This reaction involves the conversion of liquid nitrogen to gaseous nitrogen. At room temperature (25°C), nitrogen exists as a gas. Therefore, the reaction of converting nitrogen from its liquid state to its gaseous state is spontaneous at 25°C.

Reaction (c): C6H12O6(s) → C6H12O6(l) at 25°C

This reaction involves converting glucose from its solid state to liquid state. The melting point of glucose is 146°C, which is significantly higher than the temperature given (25°C). Glucose cannot exist as a liquid at 25°C; therefore, this reaction is not spontaneous.

Reaction (d): Ca²⁺(aq) + CO3²⁻(aq) → CaCO3(s)

In this reaction, calcium carbonate precipitates out of the solution as a solid. Calcium carbonate has low solubility in water and is known to precipitate in the presence of calcium ions. The products are more stable than the reactants in this case, which means the reaction is thermodynamically favorable. Therefore, this reaction is spontaneous.

Key concepts

Entropy and Spontaneous Reactions

Entropy, symbolized by the letter 'S', is a measure of the disorder or randomness of a system. In terms of chemical reactions, the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. This means that a process where the entropy of the system increases is generally favorable and thus, more likely to be spontaneous.

Spontaneous reactions are those that occur without external intervention. In the context of chemistry, spontaneous reactions often lead to an increase in entropy. For example, the conversion of a solid to a liquid or gas, or the mixing of two gases, increases disorder and therefore tends to be spontaneous, assuming temperature and pressure conditions are favorable.

No matter how complex the reaction, the fundamental question about spontaneity always comes back to whether the process results in an increase in the total entropy of the system and its surroundings.

Chemical Reaction Spontaneity

The spontaneity of a chemical reaction is determined by its Gibbs free energy change (\( \triangle G \)), which combines entropy (\( S \)) and enthalpy (\( H \)) changes according to the equation \( \triangle G = \triangle H - T\triangle S \). A negative \( \triangle G \) indicates a spontaneous reaction, while a positive \( \triangle G \) indicates a non-spontaneous one.

For reaction (a), even though forming a gas from a solid could increase entropy, the actual conversion of lead oxide to lead requires energy input to proceed, indicating \( \triangle G \) is not negative under standard conditions without external input. In reaction (d), the formation of a solid from aqueous ions represents a decrease in entropy, but the overall stability of the products leads to a negative \( \triangle G \), and thus, the reaction is spontaneous. This demonstrates how changes in enthalpy and entropy are both critical when considering reaction spontaneity.

Thermodynamics in Chemistry

Thermodynamics is a branch of physics that deals with heat, work, and forms of energy. In chemistry, thermodynamics primarily concerns itself with the study of energy changes that occur during chemical reactions and phase transitions.

Energy changes in reactions can be understood through concepts such as enthalpy (\( H \)), which reflects the heat absorbed or released, and entropy (\( S \)), which is associated with the disorder of the molecules involved. The interplay of these two quantities defines the thermodynamic favorability of a reaction. For instance, while reaction (c) would usually lead to an entropy increase due to solid-liquid transition, the fact that it is not physically possible for glucose to melt at the temperature given indicates that the entropic considerations cannot override the thermodynamic constraints set by temperature.

Solid-Liquid-Gas Phase Transitions

Phase transitions are transformations from one state of matter to another, such as from solid to liquid (melting), liquid to gas (vaporization), or solid to gas (sublimation). The entropy typically increases during these transitions since the molecules in a solid are more ordered than in a liquid, and even less ordered in a gas.

For a phase transition to occur spontaneously at a given temperature, the substance must reach a particular point known as the transition temperature. For example, in reaction (b), nitrogen in its liquid form spontaneously turns into a gas at room temperature because that is below nitrogen's boiling point. On the contrary, in reaction (c), glucose remains a solid at 25°C because this temperature is well below its melting point, highlighting the importance of phase transition temperatures in determining whether a particular change of state can be spontaneous.