Question

In which of the following systems is (are) work done by the surroundings on the system? Assume pressure and temperature are constant. a. \(2 \operatorname{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \operatorname{SO}_{3}(g)\) b. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) c. \(4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) e. \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaCO}(s)+\mathrm{CO}_{2}(g)\)

Short answer

Work is done by the surroundings on the system in systems a and c, as the final number of moles of gas is lower than the initial number of moles in these systems.

Step-by-step solution

Observe the change in the number of moles of gas

For each given system, identify and compare the initial and final number of moles of gas. a. $2 \operatorname{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \operatorname{SO}_{3}(g)$ Initial moles of gas: 3 Final moles of gas: 2 b. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) Initial moles of gas: 0 Final moles of gas: 1 c. $4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$ Initial moles of gas: 11 Final moles of gas: 10 d. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) Initial moles of gas: 1 Final moles of gas: 2 e. \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaCO}(s)+\mathrm{CO}_{2}(g)\) Initial moles of gas: 0 Final moles of gas: 1

Determine the systems where work is done by the surroundings on the system

Work is done by the surroundings on the system if the final number of moles of gas is lower than the initial number of moles. a. Initial moles of gas: 3, Final moles of gas: 2 (the number of moles of gas decreases) b. Initial moles of gas: 0, Final moles of gas: 1 (the number of moles of gas increases) c. Initial moles of gas: 11, Final moles of gas: 10 (the number of moles of gas decreases) d. Initial moles of gas: 1, Final moles of gas: 2 (the number of moles of gas increases) e. Initial moles of gas: 0, Final moles of gas: 1 (the number of moles of gas increases) Based on the analysis above, systems a and c are the cases where work is done by the surroundings on the system.

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and formation of chemical bonds. Let's explore this concept with the example given in option (a), where sulfur dioxide (\( \text{SO}_2 \)) reacts with oxygen (\( \text{O}_2 \)) to form sulfur trioxide (\( \text{SO}_3 \)). During this chemical process, molecules rearrange themselves to form new products.
One important aspect to observe in the reactions is the type of substances involved—whether they are solids, liquids, or gases. These states can influence the reaction properties, especially when considering the effect on moles and pressure. Chemical reactions are not just limited to combining elements or compounds; they also involve conservation of mass and energy changes.
In essence, understanding these transformations requires knowing what molecules take part, what changes occur, and the conditions under which the changes happen, such as temperature and pressure.

Moles of Gas

The concept of 'moles of gas' is crucial in thermodynamics, especially when discussing gas reactions. The mole is a standard unit in chemistry that quantifies the number of particles. When reactions involve gases, comparing initial and final moles helps predict whether the gas volume will increase or decrease.
For example, in option (c), we have a change from 11 moles of gas on the reactant side to 10 moles on the product side. Subtracting moles indicates a reduction, which typically points to a situation where the surroundings might be doing work on the system. This concept is framed by the Ideal Gas Law, linking moles of gas with other variables like pressure and volume.
To apply this in practical situations, always write down the balanced chemical equation, and then count moles only for the gases present. This systematic counting reveals much about the behavior of gases in the chemical reaction.

Pressure and Temperature Effects

Pressure and temperature are two significant factors affecting gas reactions. In thermodynamics, these factors influence how gases expand or compress, subsequently affecting work and energy transfer.
Consider when the moles of gas decrease, as in option (a). As the final moles decrease, the gas might exert less outward pressure, which implies that the system might have experienced compression due to constant temperature and pressure conditions.
When analyzing reactions, such as turning a solid into a gas (option b), an increase in gas moles causes expansion, indicating energy absorption from surroundings to do the work. However, when reaction conditions, like pressure and temperature, remain unchanged, any change in gas moles means work is being done – either by or against the surroundings.
Understanding the interplay of pressure and temperature with the number of moles helps predict how energy moves in these systems and helps anticipate the nature of work done during chemical processes.