Question

In: Chemistry

Estimate the final temperature in C when 2.34 moles of oxygen gas is isenthalpically expanded to 10 times its initital volume, starting at standard conditions, which in this case is 298K and 1atm

Estimate the final temperature in C when 2.34 moles of oxygen gas is isenthalpically expanded to 10 times its initital volume, starting at standard conditions, which in this case is 298K and 1atm. I know the Joule-Thomson coeffecient for oxygen under these conditions is 0.31Katm^-1. 

Solutions

Expert Solution

given moles of gas = 2.4, T= 298K, P=1 atm, V = volume at standard conditions = nRT/P = 2.4*0.0821*298/1= 58.72 L, the volume is expaned to 10 times the orginal volume, New volume, V2= 587.2L

From gas law, Pressure after expansion= nRT/V= 2.4*0.0821*T/582.7 L=0.000338T

for isoenthalpic expansion

(dT/dP)H= joules thomson coefficient = 0.31

dT =0.31* (1-0.000338T)

dT/ (1-0.000338T)=0.31

when integrated between T1= 298K and T2 =final temperature

-ln(1-.000338T2/(1-0.000338T1)= 0.31*0.000338

-ln(1-0.000338T2)/(1-0.000338*298)= 0.000105

(1-0.000338T2)/(1-.000338*298)= 0.9989

1-0.000338T2= 0.8992

T2= 265.3K


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