Question

Calculate the work done in each of the following reactions. State whether work is done on or by the system.

(a) The oxidation of one mole of SO₂ at 50°C.

2SO_2(g)  + O_2(g)  → 2SO_3(g)

(b) Decomposition of 2 moles of NH₄NO₃ at 100°C

NH₄NO_3(s)  → N₂O_(g) + 2H₂O_(g)

Answer 1

(a) Given reaction :

2SO_2(g)  + O_2(g)  → 2SO_3(g)

For 1 mole of SO₂,

SO_2(g)  + \(\frac{1}{2}\)O_2(g)  → SO_2(g)

∴ Δn = (n₂)_{gaseous products}  – (n₁)_{gaseous reactants}

= 1 - (1 + \(\frac{1}{2}\))

= -0.5 mol

Since there is decrease in number of moles of gases, there will be compression, hence, the work will be done on the system by the surroundings. 

Work is given by,

∴ W = – ΔnRT 

= – (- 0.5) × 8.314 × (273 + 50) 

= + 1342.7 J

(b) Given reaction :

NH₄NO_3(s)  → N₂O_(g) + 2H₂O_(g)

For 2 moles of NH₄NO₃,

2NH₄NO_3(s)  → 2N₂O_(g) + 4H₂O_(g)

∴ Change in number of moles,

∴ Δn = (n₂)_{gaseous products}  – (n₁)_{gaseous reactants}

= (2 + 4) – 0 

= 6 mol

Since there is an increase in number of moles of gases, work of expansion is done by the system on the surroundings.

∴ W = -ΔnRT 

= – 6 × 8.314 × (273+ 100) 

= – 18606 J 

= – 18.606 kJ