Question

Consider the following changes: a. \(\mathrm{N}_{2}(g) \longrightarrow \mathrm{N}_{2}(l)\) b. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g)\) c. \(\mathrm{Ca}_{3} \mathrm{P}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 3 \mathrm{Ca}(\mathrm{OH})_{2}(s)+2 \mathrm{PH}_{3}(g)\) d. \(2 \mathrm{CH}_{3} \mathrm{OH}(l)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\) e. \(\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)\) At constant temperature and pressure, in which of these changes is work done by the system on the surroundings? By the surroundings on the system? In which of them is no work done?

Short answer

In summary, work is done by the system on the surroundings (expansion work) in reactions c and e, work is done by the surroundings on the system (compression work) in reactions a and d, and no work is done in reaction b.

Step-by-step solution

Determine the change in the number of gas molecules in each reaction

Since we are looking for work done at constant temperature and pressure, the only type of work we need to consider is expansion or compression work. Expansion work occurs when there is an increase in the number of gas molecules, and compression work occurs when there is a decrease in the number of gas molecules. To determine the type of work done for each reaction, we need to compare the number of gas molecules before and after the reaction: a. N2(g) → N2(l): 1 gas molecule before, 0 gas molecules after b. CO(g) + H2O(g) → H2(g) + CO2(g): 2 gas molecules before, 2 gas molecules after c. Ca3P2(s) + 6 H2O(l) → 3 Ca(OH)2(s) + 2 PH3(g): 0 gas molecules before, 2 gas molecules after d. 2 CH3OH(l) + 3 O2(g) → 2 CO2(g) + 4 H2O(l): 3 gas molecules before, 2 gas molecules after e. I2(s) → I2(g): 0 gas molecules before, 1 gas molecule after

Determine the type of work done for each reaction

Now we can determine the type of work done (if any) for each reaction based on the changes in the number of gas molecules: a. Since the number of gas molecules decreases, work is done by the surroundings on the system (compression work). b. Since there is no change in the number of gas molecules, no work is done. c. Since the number of gas molecules increases, work is done by the system on the surroundings (expansion work). d. Since the number of gas molecules decreases, work is done by the surroundings on the system (compression work). e. Since the number of gas molecules increases, work is done by the system on the surroundings (expansion work). Now, we can summarize the results: Work done by the system on the surroundings (expansion work): reactions c and e Work done by the surroundings on the system (compression work): reactions a and d No work done: reaction b

Key concepts

Expansion and Compression Work

Understanding the role that gases play in the work done during a chemical reaction can be quite fascinating. In the context of chemistry, when we talk about expansion and compression work, we're referring to the physical work that's performed when a gas expands or is compressed during a reaction at constant temperature and pressure.

For example, picture a balloon being filled with air. As the number of gas molecules inside the balloon increases, they push against the walls of the balloon, causing it to expand. This expansion is similar to the work done by a system on its surroundings during a chemical reaction when the number of gas molecules increases. Conversely, if we were to squeeze the balloon, reducing its volume, we'd be doing compression work, which is analogous to the surroundings doing work on the system when there's a decrease in the number of gas molecules.

Let's consider reaction 'c' mentioned in the exercise: \(\mathrm{Ca}_{3} \mathrm{P}_{2}(s) + 6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 3 \mathrm{Ca}(\mathrm{OH})_{2}(s) + 2 \mathrm{PH}_{3}(g)\). Here, we notice the production of gas molecules, indicating that the system is doing expansion work on the surroundings. On the other hand, in reaction 'a', \(\mathrm{N}_{2}(g) \longrightarrow \mathrm{N}_{2}(l)\), there's a decrease in gas molecules as it becomes liquid, so the surroundings are doing compression work on the system.

Gas Molecule Changes

When analyzing gas molecule changes during a chemical reaction, it's paramount to consider the state of matter of the reactants and products. The state (solid, liquid, or gas) determines how molecules interact and move within the system. During a chemical reaction, when substances change from one state to another, the number of gas molecules present can either increase or decrease, and this directly affects whether work is performed and the type of work involved.

For instance, reaction 'e' in the exercise, \(\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(g)\), illustrates a simple phase change from solid to gas. This process increases the free-moving gas molecules in the system and causes expansion work to be done by the system on the surroundings, as the gas molecules exert force when moving apart. It's critical to understand that only gases contribute significantly to expansion or compression work due to their ability to expand freely and exert pressure on the surroundings.

In contrast, in reaction 'd', \(2 \mathrm{CH}_{3} \mathrm{OH}(l) + 3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) + 4 \mathrm{H}_{2} \mathrm{O}(l)\), the number of gas molecules decreases, indicating that the surroundings are doing work on the system through compression. These concepts underline the dynamic nature of molecules in their different states and their role in the energy exchange of a chemical system.

Chemical Thermodynamics

Chemical thermodynamics is the branch of physical chemistry concerned with the relationship between chemical reactions and the laws of thermodynamics. The main goal here is to understand how energy is transformed during reactions and how these transformations dictate the direction and extent of chemical processes.

In a thermodynamic system, work and heat are the two main forms of energy transfer. The first law of thermodynamics, also known as the conservation of energy, states that energy cannot be created or destroyed, only transformed or transferred. In chemical reactions, such as those listed in the exercise, expansion and compression work involve the transformation of energy from the chemical potential of the reactants to mechanical energy that is either absorbed or released by the system.

When considering the reactions where no work is done, it's important to realize that this doesn't mean that no energy changes are occurring; it simply means that, in terms of gas expansion or compression, there is no net work being done on or by the system. This is seen in reaction 'b', where the number of gas molecules remains the same before and after the reaction, highlighting the importance of gases in the energy balance of chemical thermodynamics.