Question

For each of the following processes, predict the algebraic sign of \(\Delta_{\mathrm{r}} H^{\circ}, \Delta_{\mathrm{r}} S^{\circ},\) and \(\Delta_{\mathrm{r}} G^{\circ} .\) No calculations are necessary; use your common sense. (a) The decomposition of liquid water to give gaseous oxygen and hydrogen, a process that requires a considerable amount of energy. (b) Dynamite is a mixture of nitroglycerin, \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{N}_{3} \mathrm{O}_{9}\) and diatomaceous earth. The explosive decomposition of nitroglycerin gives gaseous products such as water, \(\mathrm{CO}_{2},\) and others; much heat is evolved. (c) The combustion of gasoline in the engine of your car, as exemplified by the combustion of octane. $$2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{g})+25 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$

Short answer

(a) ΔrH° > 0, ΔrS° > 0, ΔrG° > 0; (b) ΔrH° < 0, ΔrS° > 0, ΔrG° < 0; (c) ΔrH° < 0, ΔrS° > 0, ΔrG° < 0.

Step-by-step solution

Predicting the sign of ΔrH° for Process (a)

The decomposition of liquid water into gaseous hydrogen and oxygen requires significant energy input (endothermic process). Therefore, the enthalpy change ΔrH° is positive.

Predicting the sign of ΔrS° for Process (a)

The process involves going from one liquid to two gases, increasing molecular disorder. Therefore, the entropy change ΔrS° is positive.

Predicting the sign of ΔrG° for Process (a)

Since ΔrH° is positive and ΔrS° is positive, but the process is not spontaneous at standard conditions without energy input, ΔrG° is positive.

Predicting the sign of ΔrH° for Process (b)

The explosive decomposition of nitroglycerin releases a lot of energy (exothermic process). Therefore, the enthalpy change ΔrH° is negative.

Predicting the sign of ΔrS° for Process (b)

The decomposition results in gaseous products, increasing randomness. Thus, the entropy change ΔrS° is positive.

Predicting the sign of ΔrG° for Process (b)

Both ΔrH° is negative and ΔrS° is positive, making the process spontaneous at standard conditions, so ΔrG° is negative.

Predicting the sign of ΔrH° for Process (c)

Combustion is an exothermic reaction, so the entropy change ΔrH° is negative.

Predicting the sign of ΔrS° for Process (c)

The combustion of gasoline (octane) produces more gas molecules (CO₂ and H₂O), increasing disorder; hence, ΔrS° is positive.

Predicting the sign of ΔrG° for Process (c)

With both ΔrH° negative and ΔrS° positive, the combustion of octane is spontaneous, making ΔrG° negative.

Key concepts

Enthalpy Change

Enthalpy change, represented as \(ΔH^{\circ}\), is a measure of heat energy that is either absorbed or released during a chemical reaction. In thermodynamics, this concept helps us predict whether a reaction will be endothermic (absorbing heat) or exothermic (releasing heat).

**Endothermic Reactions**: These reactions require energy to proceed, meaning they absorb heat. An example is the decomposition of liquid water into gaseous oxygen and hydrogen. Since energy input is necessary, \(ΔrH^{\circ}\) for this reaction is positive.

**Exothermic Reactions**: Contrary to endothermic reactions, exothermic processes release energy, often in the form of heat. For instance, the explosive decomposition of nitroglycerin demonstrates an exothermic change, as it releases a significant amount of energy. Thus, \(ΔrH^{\circ}\) for such processes is negative. Similarly, the combustion of octane, used in engines, is also exothermic, leading to a negative \(ΔrH^{\circ}\).

Entropy Change

Entropy change, denoted by \(ΔS^{\circ}\), represents the degree of disorder or randomness within a system. When a chemical reaction occurs, the arrangement and motion of molecules often change, affecting the entropy.

**Increasing Entropy**: When a system's disorder increases, \(ΔS^{\circ}\) becomes positive. For example, converting liquid water into gases such as hydrogen and oxygen increases molecular disorder—leading to a positive \(ΔrS^{\circ}\). Similarly, the decomposition of nitroglycerin and combustion of octane boost the number of gaseous products, thus increasing entropy.

**Decreasing Entropy**: Although not illustrated in the provided examples, reactions where gases form liquids or solids indicate a decrease in randomness and lead to negative \(ΔrS^{\circ}\). Situations like these are less typical in explosive or combustion reactions but can occur in condensation or crystallization processes.

Gibbs Free Energy

Gibbs Free Energy, expressed as \(ΔG^{\circ}\), determines the spontaneity of a reaction—a critical factor in understanding whether a process will occur naturally under specific conditions. It is calculated using the formula: \[ΔG^{\circ} = ΔH^{\circ} - TΔS^{\circ}\], where \(T\) is the temperature in Kelvin.

**Spontaneous Reactions**: If \(ΔG^{\circ}\) is negative, the reaction is spontaneous, meaning it can proceed without an external energy source. For instance, the decomposition of nitroglycerin and the combustion of octane are both spontaneous under standard conditions because they release energy (\(ΔH^{\circ}\) negative) and increase entropy (\(ΔS^{\circ}\) positive).

**Non-spontaneous Reactions**: A positive \(ΔG^{\circ}\) value indicates a non-spontaneous process. An example can be seen in the decomposition of liquid water into gases, which requires external input of energy, thus making the process non-spontaneous under standard conditions.