The following reactions take place in a cylinder equipped...

The following reactions take place in a cylinder equipped with a movable piston at atmospheric pressure (Figure P5.27). Which reactions will result in work being done on the surroundings? Assume the system returns to an initial temperature $c$ $110^{\circ} \mathrm{C} .$ (Hint: The volume of a gas is proportional to number of moles, $n,$ at constant temperature and pressure.) a. $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow$ $\mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ b. $\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$ c. $\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$

The following reactions take place in a cylinder equipped with a movable piston at atmospheric pressure (Figure P5.27). Which reactions will result in work being done on the surroundings? Assume the system returns to an initial temperature $c$ $110^{\circ} \mathrm{C} .$ (Hint: The volume of a gas is proportional to number of moles, $n,$ at constant temperature and pressure.)
a. $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow$ $\mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
b. $\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$
c. $\mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)$

Key Concepts

Thermodynamic Work

This concept recognizes that when a system changes its volume at constant pressure, it either performs work on the surroundings (expansion) or has work done on it (compression). In an isobaric process, the amount of work is given by the product of pressure and the change in volume, linking energy transformation to mechanical work.

Stoichiometry of Gaseous Reactions

Stoichiometry in gaseous reactions involves comparing the number of moles of gas on the reactants and products sides. It is a critical tool for predicting changes in total gas moles during reactions, which in turn influences volume changes and the associated work during pressure-constant processes.

Gas Laws and Volume-Mole Relationship

This concept is based on the ideal gas law, which states that at constant temperature and pressure, the volume occupied by a gas is directly proportional to the number of moles present. Understanding this relationship allows one to deduce volume changes from stoichiometric mole differences in gaseous reactions.

Sign Convention in Thermodynamics

The sign convention establishes that work done by the system on the surroundings (expansion) is considered positive, while work done on the system (compression) is negative. Recognizing this helps in correctly interpreting the energetic outcomes of chemical reactions under constant pressure.

Isobaric Processes

An isobaric process occurs at constant pressure, meaning that any volume change directly translates into work. This is particularly relevant in systems with movable pistons, where the linkage between gas moles and volume changes dictates whether the system performs work on its surroundings.

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