Question

Which of the following processes are spontaneous: (a) the melting of ice cubes at \(-10^{\circ} \mathrm{C}\) and 1 atm pressure; (b) separating a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) into two separate samples, one that is pure \(\mathrm{N}_{2}\) and one that is pure \(\mathrm{O}_{2} ;\) (c) alignment of iron filings in a magnetic field; (d) the reaction of hydrogen gas with oxygen gas to form water vapor; (e) the dissolution of \(\mathrm{HCl}(g)\) in water to form concentrated hydrochloric acid?

Short answer

In summary, the following processes are spontaneous: (c) alignment of iron filings in a magnetic field, (d) the reaction of hydrogen gas with oxygen gas to form water vapor, and (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid. The other processes, (a) the melting of ice cubes at -10°C and 1 atm pressure and (b) separating a mixture of N2 and O2 into pure samples, are not spontaneous.

Step-by-step solution

(a) Melting of ice cubes at -10°C and 1 atm pressure

Ice normally melts at 0°C when the surrounding temperature is above the melting point. In this case, the temperature is below the melting point (-10°C), which means that the process is not favored thermodynamically. Therefore, the melting of ice cubes at -10°C and 1 atm pressure is not a spontaneous process.

(b) Separating a mixture of N2 and O2 into pure samples

Separation of a mixture of gases into pure samples requires energy input to overcome intermolecular interactions. Moreover, this process would decrease the entropy of the system, which also requires energy input. As no external energy source is specified in the exercise, we can assume that this separation process is not spontaneous.

(c) Alignment of iron filings in a magnetic field

When iron filings are exposed to a magnetic field, they align along the field lines due to their magnetic properties. This alignment process happens when the magnetic energy within the system is minimized. Therefore, we can conclude that the alignment of iron filings in a magnetic field is a spontaneous process.

(d) Reaction of hydrogen gas with oxygen gas to form water vapor

The reaction of hydrogen gas (e.g. 2H2) with oxygen gas (O2) to form water vapor (2H2O) is an exothermic reaction, meaning it releases energy in the form of heat. This reaction has a negative Gibbs free energy change, indicating that it is a spontaneous process under standard conditions.

(e) Dissolution of HCl(g) in water to form concentrated hydrochloric acid

The dissolution of HCl(g) in water to form concentrated hydrochloric acid is an exothermic process, as energy is released when the HCl molecules interact with water molecules. The process leads to an increase in entropy as the ordered gas molecules are dispersed in the more random liquid state. Given that both entropy and enthalpy favor spontaneity, we can conclude that the dissolution of HCl(g) in water is a spontaneous process.

Key concepts

Spontaneous Processes

In thermodynamics, a spontaneous process is one that occurs without an external force or influence. These processes happen naturally under given conditions, and they often result in a decrease in the energy of a system or an increase in disorder, also known as entropy. A key aspect of spontaneous processes is that they do not require additional energy to proceed. Instead, they progress as a result of favorable energy changes within the system.
Common examples of spontaneous processes include:

• The melting of ice at temperatures above its melting point
• Iron filings aligning in a magnetic field
• Chemical reactions that result in energy release, such as combustion

Understanding spontaneous processes is crucial as it helps predict whether a chemical reaction or physical change will occur under specific conditions without assistance.

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it plays a central role in determining the spontaneity of a process. The second law of thermodynamics states that the total entropy of an isolated system or the universe always increases over time.
Essentially, systems tend to move towards configurations that maximize randomness or entropy. This is why some processes happen naturally.
Consider these points about entropy:

• Processes that increase disorder, such as ice melting to water, often increase entropy.
• When a gas dissolves in a liquid, as in the dissolution of HCl in water, its molecules spread out, increasing the system's entropy.
• Decreasing entropy generally requires energy input, making such processes non-spontaneous under normal conditions.

Thus, entropy helps explain why certain changes occur spontaneously, highlighting the natural tendency towards greater disorder in the universe.

Exothermic Reactions

Exothermic reactions are chemical processes that release energy, typically in the form of heat, to the surroundings. This release of energy often makes these reactions spontaneous since they result in a decrease in the overall energy of the system.
An important characteristic of exothermic reactions is that they can lead to a drop in enthalpy (the heat content of a system). When considering spontaneity, both the decrease in enthalpy and the associated increase in entropy can drive a process forward.
Examples of exothermic reactions include:

• The burning of fuels, which releases significant heat and light
• The reaction of hydrogen gas with oxygen to form water vapor
• The dissolution of some gases like HCl in water, which releases heat

Recognizing exothermic reactions helps in understanding how energy changes make certain processes favorable and self-sustaining.

Gibbs Free Energy

Gibbs Free Energy is a thermodynamic potential that helps determine whether a process is spontaneous. It combines the effects of enthalpy (total heat content) and entropy to predict process favorability. The formula for Gibbs Free Energy is:\[ \Delta G = \Delta H - T \Delta S \]where \( \Delta G \) is the change in Gibbs Free Energy, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.
A negative value of \( \Delta G \) indicates a spontaneous process, while a positive value suggests that the process is non-spontaneous under the given conditions.
Consider these points:

• In exothermic reactions, the decrease in enthalpy can often lead to negative \( \Delta G \)
• Processes that significantly increase entropy can also result in negative \( \Delta G \)
• Gibbs Free Energy provides a comprehensive way to assess chemical reactions and physical changes

Understanding Gibbs Free Energy is essential for predicting and explaining the natural tendencies of chemical processes.