Question

Which of the following processes are spontaneous? a. Salt dissolves in \(\mathrm{H}_{2} \mathrm{O}\) . b. A clear solution becomes a uniform color after a few drops of dye are added. c. Iron rusts. d. You clean your bedroom.

Short answer

Processes a (salt dissolves in water), b (a clear solution becomes a uniform color after a few drops of dye are added), and c (iron rusts) are spontaneous. Process d (cleaning your bedroom) is not spontaneous as it requires external energy input.

Step-by-step solution

Process a: Salt dissolves in water

When salt (such as sodium chloride, NaCl) is added to water, it dissolves due to the attraction between the polar water molecules and the ions in the salt crystal. This process is driven by the decrease in Gibbs free energy, which means it is a spontaneous process. So, Process a is spontaneous.

Process b: A clear solution becomes a uniform color after a few drops of dye are added

When a few drops of dye are added to a clear solution, the dye molecules spread out evenly throughout the solution due to the random motion of the dye and solvent molecules (a process known as diffusion). This process occurs without the need for any external energy input and is driven by the increase in entropy (disorder) of the system. So, Process b is spontaneous.

Process c: Iron rusts

Rusting of iron is an oxidation process that occurs when iron comes into contact with oxygen and moisture. The oxidation of iron is spontaneous because it is exothermic (releases heat to the surroundings) and increases the entropy of the system. Iron rusts naturally without any external influence, so Process c is spontaneous.

Process d: You clean your bedroom

Cleaning your bedroom requires work and external input of energy (in this case, physical effort). This process does not happen spontaneously, as it requires an external force to be applied to clean the room. So, Process d is not spontaneous. In conclusion, Processes a, b, and c are spontaneous, while Process d is not spontaneous.

Key concepts

Gibbs Free Energy

Gibbs Free Energy is a crucial concept when it comes to understanding spontaneous processes. It is a measure of the maximum amount of work that a thermodynamic system can perform at constant temperature and pressure. The symbol for Gibbs Free Energy is G.

When considering whether a process is spontaneous, we look at the change in Gibbs Free Energy, symbolized as \( \Delta G \). If \( \Delta G \) is negative, the process is spontaneous, meaning it can occur without external energy.

For example, when salt dissolves in water, water molecules interact with salt ions, leading to a reduction in Gibbs Free Energy because the system releases free energy into the surroundings. This spontaneous process continues until equilibrium is reached. In this way, the concept of Gibbs Free Energy is essential for predicting the behavior of systems in chemical reactions and phase changes.

Entropy

Entropy is another fundamental concept in understanding spontaneous processes. It is a measure of the disorder or randomness in a system. The higher the entropy, the greater the disorder. Entropy is often symbolized by the letter S.

Spontaneous processes typically lead to an increase in the entropy of the universe. This is because nature tends to move towards states of higher disorder. For instance, when a dye is added to a clear solution, the dye particles disperse, resulting in a uniform color. This process highlights an increase in entropy as the dye molecules randomly distribute throughout the solution.

• Entropy is driven by the tendency of systems to move from ordered to disordered states.
• It is closely tied to the concept of energy dispersal.
• A good rule of thumb is that natural processes tend to increase the total entropy of the universe.

Understanding entropy helps in grasping why certain processes, like diffusion and mixing, occur spontaneously without energy input.

Diffusion

Diffusion is a process in which particles spread out from an area of high concentration to an area of low concentration. This occurs due to the random motion of molecules, and it happens spontaneously as systems tend toward equilibrium and increased entropy.

A common example of diffusion is when dye is added to water: the dye molecules spread throughout the water, resulting in a uniform distribution. This movement does not require any external energy, as it naturally occurs due to thermal motion and the drive to maximize disorder (entropy).

• Diffusion is driven by random molecular motion.
• It often occurs in gases and liquids where molecules are free to move past one another.
• This spontaneous spreading leads to a more thermodynamically stable state.

Through the lens of thermodynamics, diffusion is an excellent example of how systems work towards equilibrium, illustrating fundamental principles like entropy increase and energy distribution.

Oxidation

Oxidation is a chemical reaction that involves the transfer of electrons, typically resulting in the combination of a substance with oxygen. This process is often exothermic, meaning it releases energy, and can occur spontaneously under the right conditions.

A classic example of oxidation is the rusting of iron, where iron reacts with oxygen in the presence of water to form iron oxide (rust). This reaction is spontaneous because it releases energy in the form of heat and increases the overall entropy of the system.

• Oxidation is key to many natural processes, including combustion and metabolism.
• The tendency of a substance to lose electrons and react with oxygen provides driving force for numerous reactions.
• It is vital in everyday phenomena and industrial applications, from energy production to metal corrosion.

By understanding oxidation, we can better appreciate its role in both natural and human-made systems, making it essential to the study of chemical reactions and energy changes.