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Calculate the maximum work when 24 g ...

Calculate the maximum work when 24 g of oxygen are expanded isothermally and reversibly from a pressure of `1.6 xx 10^(5) Pa` to 100 Kpa at 298 K.

Text Solution

Verified by Experts

The correct Answer is:
`W_(max) =- 873.5 J`
Given : mass of oxygen = W= 24 g
Initial pressure `= P_(1) = 1.6 xx 10^(5) pa`
Final pressure `= P_(2) =100 kP_(a) = 100 xx 10^(3) Pa= 1 xx 10^(5) Pa`
Temperature =T = 298 K
Molar mass of oxygen `(O_(2)) = M_(O_(2)) = 32 g mol^(-1)`
`W_(max)= ?`
Number of moles of `O_(2) = n_(O_(2)) = (W)/(M_(O_(2)))= (24)/(32) = 0.75 mol`
`W_(max) = - 2.303 nRT log_(10) .(P_(1))/(P_(2))`
`=- 2.303 xx 0.75 xx 8.314 xx 298 log_(10) .(1.6 xx 10^(5))/(1xx 10^(5))`
`=- 2.303 xx 0.75 xx 8. 314 xx 298 xx log_(10) 1.6`
`=- 2.303 xx 0.75 xx 8.314 xx 298 xx 0. 2041`
`=- 873.5 J`
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