- #1
MexChemE
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Homework Statement
Find ΔH for the isothermal expansion of one mole of CO2 from a pressure of 1 atm to zero at 300 K. The critical point of CO2 is TC = 31 °C and PC = 73 atm. Use the equation for ΔH you previously derived from the Berthelot equation of state. (Answer provided by textbook: ΔH = -10.2 cal)
Homework Equations
ΔH for isothermal processes of real gases, derived in a previous problem from the Berthelot EOS:
[tex]\Delta H = \left( An + \frac{3Bn}{T^2} \right) \Delta P[/tex]
[tex]A = \frac{9RT_C}{128P_C}[/tex]
[tex]B = -\frac{27RT_C^3}{64P_C}[/tex]
The Attempt at a Solution
Calculating A and B from provided data and using R = 0.08205 L atm mol-1 K-1.
A = 0.02404 L mol-1
B = -13341.448 L K2 mol-1
If we got from 1 atm to zero, then ΔP = -1 atm. Plugging all these values into the ΔH equation gives:
[tex]\Delta H = \left( \left(0.02404 \ \frac{L}{mol} \right)(1 \ mol) + \frac{(3)(-13341.448 \ \frac{L \cdot K^2}{mol})(1 \ mol)}{(300 K)^2} \right) (-1 \ atm) = 0.4207 \ L \cdot atm[/tex]
[tex]\Delta H = 0.4207 \ L \cdot atm \ \left(\frac{24.22 \ cal}{1 \ L \cdot atm} \right) = 10.19 \ cal[/tex]
As you can see, my answer is numerically correct, but positive instead of negative as in the textbook. I've checked every part of the problem and found no error, so I don't know what should I change to get the negative value. Is my ΔP correct? I don't think the minus sign in the answer is a typo, since my intuiton is telling me the system should have a net decrease in energy (as it theoretically ended up having zero pressure), so I must be the one making a mistake. Any insight will be greatly appreciated, thanks in advance!