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Question
Calculate the work done and comment on whether work is done on or by the system for the decomposition of 2 moles of NH4NO3 at 100 °C
NH4NO3(s) → N2O(g) + 2H2O(g)
Solution
Given:
Decomposition of 1 mole of NH4NO3
Temperature = T = 100 °C = 373 K
To find:
Work done and to determine whether work is done on the system or by the system
Formula: W = - Δ ngRT
Calculation:
The given reaction is for 1 mole of NH4NO3. For 2 moles of NH4NO3, the reaction is given as follows:
2NH4NO3(s) → 2N2O(g) + 4H2O(g)
Now,
Δ ng = (moles of product gases) - (moles of reactant gases)
Δ ng = 6 - 0 = + 6 mol (∵ NH4NO3 is in solid state)
Hence,
W = - Δ ngRT
= - (+ 6 mol) × 8.314 J K-1 mol-1 × 373 K
= - 18606.75 J
= - 18.61 kJ
Work is done by the system (since W < 0).
The work done is - 18.61 kJ. The work is done by the system.
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