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02 Lecture 4 January 11 - 1/1 CHEM350 Lecture 4 Gibbs free...

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1/1 CHEM350: Lecture 4, Jan 11 2010 Gibbs free energy for nonideal gases (section 7.5 in textbook) We know from thermodynamics that the total differential for the molar Gibbs free energy G ( T , P ) has the form d G = SdT + VdP from which we obtain the relation G P T = V If we consider a process at constant temtperature T , we obtain, d G T = VdP and integrating from initial pressure P i to final pressure P f yields, d G T P = P i P = P f = V dP P = P i P = P f Using the ideal gas equation of state for V , we get Δ G ( ) T G ( T , P f ) G ( T , P i ) = RT ln P f P i . If we let the initial pressure P i be 1 bar, i.e., P i P o , we obtain G ( T , P f ) G ( T , P o ) = RT ln P f P o or G ( T , P f ) = G o ( T ) + RT ln P f P o How can we proceed for a nonideal gas? We can replace V with a more realistic expression such as the virial equation of state, P V RT = 1 + B ' 2 ( T ) P + B ' 3 ( T ) P 2 + ...
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