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 exygen gas to form water vapor at room temperature; (e) the dissolution of HCl(g) in water to form concentrated hydrochloric acid?

Short answer

Processes (a) and (b) are not spontaneous, as the melting of ice cubes at -10°C would require external heat, and separating a mixture of N2 and O2 into two separate samples would violate the second law of thermodynamics. Processes (c), (d), and (e) are spontaneous, as the alignment of iron filings in a magnetic field occurs naturally, the reaction of hydrogen gas with oxygen gas forming water vapor is exothermic and has a negative Gibbs free energy change at room temperature, and the dissolution of HCl(g) in water is both exothermic and increases entropy.

Step-by-step solution

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

Melting of ice requires an increase in temperature for the solid to liquid phase change to occur. However, the temperature given in the exercise is -10°C, which is below the freezing point of water at 1 atm pressure (0°C). Therefore, at -10°C, the ice cubes will not naturally melt without the addition of external heat. Thus, this process is not spontaneous.

Process (b): Separating a mixture of N2 and O2 into two separate samples

According to the second law of thermodynamics, a nonspontaneous process is one that results in a decrease in the entropy (randomness) of the system. In this case, separating the mixed gases into two pure samples would decrease the overall randomness of the system, which violates the second law of thermodynamics. Therefore, this process is not spontaneous, as it would require external intervention to achieve the separation.

Process (c): Alignment of iron filings in a magnetic field

When iron filings are placed in a magnetic field, they align themselves along the field lines due to the interaction between their magnetic dipoles and the external magnetic field. This process occurs naturally without any external influence, as the iron filings seek to minimize their energy by aligning with the magnetic field. Thus, this process is spontaneous.

Process (d): Reaction of hydrogen gas with oxygen gas to form water vapor at room temperature

The reaction of hydrogen gas and oxygen gas to form water vapor is given by the following equation: \(2H_{2}(g) + O_{2}(g) \rightarrow 2H_{2}O(g)\). This reaction is widely known to be exothermic, meaning it releases heat. Furthermore, when the system reaches an equilibrium state, the reaction has a negative Gibbs free energy change, indicating a spontaneous process at room temperature. Therefore, this process is spontaneous.

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

When hydrogen chloride, HCl(g), is dissolved in water, it forms a strong acid: hydrochloric acid (HCl(aq)). This dissolution process is exothermic, as it releases heat when the HCl molecules interact with the water molecules. Additionally, this process results in an increase in the entropy of the system, as the HCl molecules become dispersed within the water. Both an increase in entropy and a decrease in enthalpy are factors that favor the spontaneity of the process. Therefore, this process is spontaneous.

Key concepts

Thermodynamics

Understanding thermodynamics is pivotal to grasping why certain processes are spontaneous. It's the branch of physics that deals with heat and temperature and their relation to energy and work. The fundamental principles of thermodynamics can determine the direction of a process and whether it will proceed without external intervention. There are four laws, with the second law specifically stating that the total entropy - a measure of disorder or randomness - of an isolated system can never decrease over time. This law is crucial when determining the spontaneity of processes such as melting ice or separating gas mixtures. A spontaneous process increases the entropy of the universe, reflecting the natural tendency towards greater disorder.

Entropy

Let's delve deeper into the concept of entropy. Entropy is essentially a quantitative measure of disorder or randomness in a system. The law of increased entropy — that the total entropy of a closed system cannot decrease — is a way of expressing the second law of thermodynamics. When looking at spontaneous processes, such as the dissolution of HCl(g) in water or the alignment of iron filings in a magnetic field, an increase in entropy frequently occurs. For example, when HCl gas dissolves, the molecules spread out from a concentrated state to a more dispersed solution, indicating an increase in entropy and thus favoring spontaneity.

It is important to puzzle out the entropy aspect in chemical reactions because it helps predict whether a reaction will occur spontaneously. A general rule of thumb: if a process increases the entropy of the system (or the universe), it has a greater chance of being spontaneous.

Gibbs Free Energy

Next on our list is Gibbs free energy, represented by the symbol G. It combines enthalpy (total heat content) and entropy to determine the spontaneity of a process under constant pressure and temperature. The Gibbs free energy equation is given by: \[ G = H - TS \] where G is Gibbs free energy, H is enthalpy, T is temperature in Kelvin, and S is entropy. If the change in Gibbs free energy (\(\Delta G\)) for a process is negative, it indicates a spontaneous process, such as the formation of water from hydrogen and oxygen gases. This powerful tool allows us to predict whether a phase change or chemical reaction will occur without external energy input. As students tackle their homework, understanding how to apply \(\Delta G\) to various processes can elucidate why certain reactions occur without assistance.

Phase Changes

Talking about phase changes is talking about physical transformations, like the melting of ice or the boiling of water. These changes occur when matter transitions from one state (solid, liquid, gas) to another due to energy changes, which affects both the enthalpy and entropy of a system. Spontaneity in phase changes is not only about temperature but also about the prevailing pressure conditions. For example, ice melting into water below 0°C at normal atmospheric pressure is non-spontaneous because it requires an external source of heat. This is why ice cubes at \( -10^{\circ}C \) will not melt on their own. Understanding how temperature and pressure affect phase changes is important for students who need to predict the behavior of substances under different environmental conditions.

Chemical Reactions

Lastly, we have chemical reactions, the process where substances, the reactants, undergo chemical transformation to form new substances, the products. Reactions can absorb or release energy, and the direction of a reaction is often predicted by looking at the Gibbs free energy change. A spontaneous reaction, such as the combination of hydrogen and oxygen to form water, typically releases energy, which may be heat in exothermic reactions. Students will frequently encounter chemical equations and calculations related to spontaneity in their homework. Understanding the relationship between reaction conditions, such as temperature and pressure, and spontaneity helps in grasping the practical aspects of thermochemistry and kinetics in their studies.