Question

Consider the processes $$ \begin{array}{l} \mathrm{H}_{2} \mathrm{O}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(l) \\ \mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{2} \mathrm{O}(g) \end{array} $$ a. Which process is favored by energy spread? Explain. b. Which process is favored by matter spread? Explain. c. How does temperature affect which process is favored? Explain.

Short answer

The process favored by energy spread is the transition from liquid water to gaseous water due to the increase in entropy. The process favored by matter spread is also the transition from liquid water to gaseous water, as the matter is more spread out in a gaseous state. Temperature affects the favorability of the processes: at low temperatures, the transition from gaseous water to liquid water is favored, while at high temperatures, the transition from liquid water to gaseous water is favored.

Step-by-step solution

a. Identifying the process favored by energy spread

To determine which process is favored by energy spread, we need to analyze the change in entropy during each process. Entropy is a measure of the spread of energy in a system, and a process with a greater entropy change will be more favored by energy spread. For the process where water changes from gaseous state to liquid state: \(H_2O(g) \rightarrow H_2O(l)\) The entropy in this process decreases, as molecules in the gaseous state have more freedom to move around than in the liquid state. For the process where water changes from liquid state to gaseous state: \(H_2O(l) \rightarrow H_2O(g)\) Entropy increases in this process, as the molecules in the gaseous state have more freedom to move around and occupy more volume than in a liquid state. Therefore, the process that is favored by energy spread is the transition from liquid water to gaseous water due to the increase in entropy.

b. Identifying the process favored by matter spread

Matter spread is related to the increase in the number of particles in the system. In both processes, the number of particles remains the same, as water molecules are conserved. The key difference between the two processes is the distribution of the molecules in each state. In the gaseous state, water molecules occupy a larger volume and are more spread out than in the liquid state. Therefore, the process that is favored by matter spread is the transition from liquid water to gaseous water, as the matter is more spread out in a gaseous state.

c. Analyzing the effect of temperature on process favorability

The favorability of a process depends on the Gibbs free energy change, which is given by the equation: \(ΔG = ΔH - TΔS\) Where ΔG is the Gibbs free energy change, ΔH is the enthalpy change, T is the temperature, and ΔS is the entropy change. In the process where water changes from gaseous state to liquid state: \(H_2O(g) \rightarrow H_2O(l)\) ΔH is negative (exothermic) as heat is released when water condenses, and ΔS is also negative as entropy decreases. In the process where water changes from liquid state to gaseous state: \(H_2O(l) \rightarrow H_2O(g)\) ΔH is positive (endothermic) as heat is absorbed when water evaporates, and ΔS is positive as entropy increases. At low temperatures, the term -TΔS in the Gibbs free energy equation is relatively small, so the exothermic process (\(H_2O(g) \rightarrow H_2O(l)\)) is favored. At high temperatures, the term -TΔS becomes larger, making the endothermic process (\(H_2O(l) \rightarrow H_2O(g)\)) more favored. In conclusion, at low temperatures, the process favored is the transition from gaseous water to liquid water, while at high temperatures, the process favored is the transition from liquid water to gaseous water.

Key concepts

Entropy

Entropy is a central topic in thermodynamics, reflecting how energy is spread out in a system. In any process, one can consider the change in entropy, which can signify whether the process is favored by the energy spread. When water transitions from gas to liquid, entropy decreases because gas molecules are more disordered and can move freely, while liquid molecules are more constrained.
In contrast, when water turns from a liquid into a gas, entropy increases. The molecules spread out more in the gaseous state, leading to a higher degree of disorder or randomness. Therefore, processes that lead to an increase in entropy, like liquid turning into gas, are generally favored in terms of energy distribution.

Gibbs Free Energy

Gibbs free energy is a measure that helps determine which chemical processes will spontaneously occur under constant temperature and pressure. It is calculated using the equation \[ ΔG = ΔH - TΔS \]where \( ΔG \) represents the Gibbs free energy change, \( ΔH \) is the enthalpy change, \( T \) is the temperature, and \( ΔS \) is the entropy change.
When the process \(H_2O(g) \rightarrow H_2O(l)\) occurs, water releases energy (negative \( ΔH \)), making it exothermic, and its entropy decreases (negative \( ΔS \)). This means at lower temperatures, where \(-TΔS\) isn't dominating the equation, this process will have a negative \( ΔG \) and thus, is favored. Conversely, when water evaporates, \(H_2O(l) \rightarrow H_2O(g)\), it absorbs energy (positive \( ΔH \)) and increases entropy (positive \( ΔS \)). At higher temperatures, this evaporation process is favored due to a larger \( -TΔS \).

Phase Changes

Phase changes, like those between gas and liquid states of water, are intriguing because they involve shifts in energy and entropy. During these changes, water molecules either gain or lose energy, which doesn't change the number of molecules, but changes how they're arranged and how they behave.
When water vapor condenses, it releases heat and its molecules become less spread out - entropy decreases. Conversely, when water evaporates, it consumes heat, and molecules become more spread out - increasing entropy. The balance of these energy exchanges is what causes one phase to be more favorable than the other under certain conditions.

Temperature Effects

Temperature plays a crucial role in determining the favorability of phase changes. It influences the Gibbs free energy through the \( -TΔS \) term in its equation. At low temperatures, the disordering effect (entropy factor) is less significant, leading to a favorable condensation of gas to liquid as it releases energy.
On the other hand, at high temperatures, entropy becomes more influential because the \( TΔS \) term grows larger. As a result, at higher temperatures, processes that increase entropy, such as the evaporation of liquid to gas, become more favorable. Thus, temperature can either dampen or enhance the effects of entropy change, swinging the favorability between condensation and evaporation.