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. \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaCO}(s)+\mathrm{CO}_{2}(g)\)

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

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.