Question

In which of the following systems is(are) work done by the surroundings on the system? Assume pressure and temperature are constant. a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) 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

Reactions b, d, and e show work being done by the surroundings on the system.

Step-by-step solution

Analyze each reaction and determine the change in the number of moles of gas

For each reaction, we will identify the number of moles of gas on the reactant side and the product side. Then, we will determine if there is an increase, decrease, or no change in the number of moles of gas. a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) Reactants: 2 moles of SO₂ gas + 1 mole of O₂ gas = 3 moles of gas Products: 2 moles of SO₃ gas Change: Decrease in the number of moles of gas. b. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) Reactants: 0 moles of gas (CO₂ is in solid form) Products: 1 mole of CO₂ gas Change: Increase in the number of moles of gas. c. \(4 \mathrm{NH}_{3}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) Reactants: 4 moles of NH₃ gas + 7 moles of O₂ gas = 11 moles of gas Products: 4 moles of NO₂ gas + 6 moles of H₂O gas = 10 moles of gas Change: Decrease in the number of moles of gas. d. \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) Reactants: 1 mole of N₂O₄ gas Products: 2 moles of NO₂ gas Change: Increase in the number of moles of gas. e. \(\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)\) Reactants: 0 moles of gas (both CaCO₃ and CaO are solids) Products: 1 mole of CO₂ gas Change: Increase in the number of moles of gas.

Identify reactions where work is done by the surroundings on the system

From the previous step, we can see that reactions b, d, and e resulted in an increase in the number of moles of gas. Therefore, work is done by the surroundings on the system in these reactions. Answer: Reactions b, d, and e show work being done by the surroundings on the system.