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Question
Answer the following question.
Calculate the maximum work when 24 g of O2 are expanded isothermally and reversibly from the pressure of 1.6 bar to 1 bar at 298 K.
Solution
Given:
Mass of O2 = 24 g
Initial pressure = P1 = 1.6 bar
Final pressure = P2 = 1 bar
Temperature = T = 298 K
To find: Maximum work (Wmax)
Formula: `"W"_"max" = - 2.303 "nRT" log_10 "P"_1/"P"_2`
Calculation:
Number of moles of O2 = n = `(24 "g")/(32 "g mol"^-1)` = 0.75 mol
Gas constant = R = 8.314 J K–1 mol–1
Now, using formula,
`"W"_"max" = - 2.303 "nRT" log_10 "P"_1/"P"_2`
= - 2.303 × 0.75 mol × 8.314 J K-1mol-1 × 298 K × `log_10 1.6/1`
= - 2.303 × 0.75 × 8.314 J × 298 × 0.2041
= - 873.4 J
The maximum work done is – 873.4 J.
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