Question

A certain reaction has $\mathrm{\Delta }{H}^{\circ }=+23.7\mathrm{kJ}$ and $\mathrm{\Delta }{5}^{\circ }=+52.4\mathrm{J}/\mathrm{K}$. (a) Is the reaction exothermic or endothermic? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (c) Calculate $\mathrm{\Delta }{G}^{\circ }$ for the reaction at $298\mathrm{K}$. (d) Is the reaction spontaneous at $298\mathrm{K}$ under standard conditions?

Short answer

(a) The reaction is endothermic. (b) The reaction leads to an increase in the randomness or disorder of the system. (c) $\Delta G°=+8.0848\text{kJ}$ (d) The reaction is non-spontaneous at 298 K under standard conditions.

Step-by-step solution

(a) Reaction type: exothermic or endothermic?

Given ΔH° = +23.7 kJ, since the sign is positive, it means the reaction is endothermic, as it absorbs heat from the surroundings.

(b) Effect on randomness or disorder

Given ΔS° = +52.4 J/K, since the sign is positive, it means the reaction leads to an increase in the randomness or disorder of the system.

(c) Calculate ΔG° for the reaction at 298 K

To calculate ΔG°, we use the formula: $\Delta G°=\Delta H°-T\Delta S°$ First, we need to convert ΔS° to kJ/K: $\Delta S°=+\frac{52.4}{1000}=+0.0524\text{kJ/K}$ Now, we plug in the values: $\Delta G°=(+23.7\text{kJ})-(298\text{K})(+0.0524\text{kJ/K})$ $\Delta G°=+23.7\text{kJ}-15.6152\text{kJ}$ $\Delta G°=+8.0848\text{kJ}$

(d) Spontaneity of the reaction at 298 K

Since ΔG° is positive, the reaction is non-spontaneous under standard conditions at 298 K.

Key concepts

Enthalpy (H)

Enthalpy, symbolized by H, is a measure of total energy of a thermodynamic system, often thought of as the 'heat content'. It accounts for the internal energy of the system along with the product of its pressure and volume. In chemistry, when a reaction occurs at constant pressure, the change in enthalpy, denoted as ΔH, reflects the heat absorbed or released.

If ΔH is positive, as seen with our example of +23.7 kJ, the reaction is endothermic, absorbing heat from the surroundings; this implies a requirement of energy input for the reaction to proceed. Conversely, a negative ΔH indicates an exothermic reaction where energy is released into the surroundings. Understanding whether a reaction is endo- or exothermic is crucial for predicting the energy implications in chemical processes, like those occurring in living organisms or industrial systems.

Entropy (S)

Entropy, represented by S, is a concept that describes the disorder or randomness within a system. It's a central principle in thermodynamics with significant implications for chemistry. The change in entropy, ΔS, tells us whether a system becomes more or less ordered as a reaction proceeds.

A positive ΔS indicates an increase in randomness, as we see with our given ΔS° of +52.4 J/K, revealing that the reaction leads to a more disordered state. This is common in reactions where the number of gaseous molecules increases or solids dissolve in solvents. An increase in entropy is often associated with favorable natural processes since systems tend to evolve toward higher entropy states.

Gibbs Free Energy (G)

Gibbs free energy (G) is arguably the most pivotal term for understanding chemical reaction spontaneity. It combines the concepts of enthalpy and entropy to determine whether a process will occur without external input (spontaneity). Defined by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin, this value provides insight into the system's energy balance.

In our calculation, ΔG° is positive (+8.0848 kJ), suggesting that under standard conditions at 298 K, the reaction is not spontaneous. It would need external energy to proceed. Any reaction with a negative ΔG° would be considered spontaneous, running of its own accord. Thus, Gibbs free energy guides chemists not only in predicting reaction spontaneity but also in designing processes that harness or change the flow of energy efficiently.

Reaction Spontaneity

Reaction spontaneity determines whether a chemical reaction will occur under particular conditions without external intervention. Spontaneity is dictated by changes in enthalpy and entropy, as combined into the Gibbs free energy change, ΔG. A negative ΔG indicates a spontaneous reaction, while a positive value indicates non-spontaneity.

In the exercise, we've deduced that the reaction in question is non-spontaneous at 298 K because ΔG° is positive. However, it's key to remember that spontaneity does not equate to reaction speed. A reaction can be spontaneous and still occur over a vast timescale, requiring a catalyst to speed up the process. Understanding these nuances is critical in fields ranging from biochemical pathways to industrial chemical production.