Questions: Part IV. Essay. 10 Points. Please answer the following as complete as possible. 20. Entropy is a fantastically important concept in thermodynamics and thus it is the focus of one of the laws of thermodynamics (the 2nd one). Tell me why understanding entropy is important in life and death, and chemistry. Use specific examples, equations, and relationships to other chemical concepts. Extra credit (+1): If the ΔG for the reaction C(s, diamond) → C(s, graphite) is -3 kJ, how come are diamonds not spontaneously turning into graphite?

Understanding the importance of entropy in life, death, and chemistry.

Definition and significance of entropy.

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it is a central concept because it helps predict the direction of spontaneous processes. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. This principle is crucial in understanding natural processes, such as the flow of heat from hot to cold bodies and the tendency of systems to move towards equilibrium.

Entropy in life and death.

In biological systems, entropy plays a vital role in maintaining life. Living organisms maintain low entropy by consuming energy and matter from their environment, which increases the entropy of the surroundings. This balance is essential for sustaining life. In death, the organized structure of living organisms breaks down, leading to an increase in entropy as the system moves towards equilibrium with its environment.

Entropy in chemistry.

In chemical reactions, entropy is a key factor in determining spontaneity. The change in entropy (\(\Delta S\)) is part of the Gibbs free energy equation: \(\Delta G = \Delta H - T\Delta S\), where \(\Delta G\) is the change in free energy, \(\Delta H\) is the change in enthalpy, and \(T\) is the temperature in Kelvin. A reaction is spontaneous if \(\Delta G\) is negative, which can occur if the entropy of the system increases.

\(\boxed{\text{Entropy is crucial for understanding the direction of natural processes, the maintenance of life, and the spontaneity of chemical reactions.}}\)

Why diamonds do not spontaneously turn into graphite despite \(\Delta G = -3 \, \text{kJ}\).

Explanation of Gibbs free energy and reaction kinetics.

The Gibbs free energy change (\(\Delta G\)) indicates the thermodynamic favorability of a reaction. A negative \(\Delta G\) suggests that the reaction is spontaneous under standard conditions. However, spontaneity does not imply that the reaction occurs quickly. The conversion of diamond to graphite is kinetically hindered due to a high activation energy barrier. This means that, although thermodynamically favorable, the reaction proceeds extremely slowly at room temperature, preventing diamonds from spontaneously turning into graphite.

\(\boxed{\text{Diamonds do not spontaneously turn into graphite because the reaction is kinetically hindered by a high activation energy barrier.}}\)

\(\boxed{\text{Entropy is crucial for understanding the direction of natural processes, the maintenance of life, and the spontaneity of chemical reactions.}}\)
\(\boxed{\text{Diamonds do not spontaneously turn into graphite because the reaction is kinetically hindered by a high activation energy barrier.}}\)