Fugacity coefficient[P(T,v)] Solve for dP as a function of dV

Vapor Fugacity From EOS

Consider a pure system IG P (P=0) as reference state Consider how we do departure functions (residual properties) Take a path

Departure (residual) Gibb’s Free Energy [v(T,P)]

Departure (residual) Gibb’s Free Energy [v(T,P)]

Fugacity coefficient[P(T,v)]

Fugacity Coefficient from EOS IF v(T,P) [i.e. virial EOS] IF P(T,v) [i.e. SRK EOS]

Practice problem (virial) Z=1+BP/RT Find the fugacity coefficient

Practice problem step 1-3 Recognize it is a vapor fugacity problem Recognize it is for a pure system Recognize I want EOS (not steam or correlation tables)

Practice problem – step 4 Choose the CORRECT equation

Practice problem – step 5 Plug in EOS into correct equation

Practice problem – step 6 Integrate and simplify

Practice problem (VDW) Z=v/(v-b)-a/RTv Find the fugacity coefficient

Practice problem step 1-3 Recognize it is a vapor fugacity problem Recognize it is for a pure system Recognize I want EOS (not steam or correlation tables)

Practice problem – step 4 Choose the CORRECT equation

Practice problem – step 5 Plug in EOS into correct equation

Practice problem – step 6 Integrate and simplify

Practice problem – step 6 Integrate and simplify

How does your book do it? vo=RT/Plow Solve for fi Set limit of Plow  0 Solve for

What about mixtures? Let’s look at pure for an analogue Change to partial molar properties

For P(T,v), do some manipulation Let’s look at the other one for a start point Change dP to dV (cyclic rule)

For P(T,v), do some manipulation Let’s look at the other one for a start point Change dP to dV (cyclic rule)

For P(T,v), do some manipulation Let’s look at the other one for a start point Plug both the real and ideal back in and adjust for difference in departure functions gdep(T,v)=gdep(T,p)+RTlnz and divide by RT to simplify into z/

Fugacity Coefficient from EOS IF v(T,P) [i.e. virial EOS] IF P(T,v) [i.e. SRK EOS]

What do they do in your book? Similar to pure but different EQ

Practice problem (VDW) Find the fugacity coefficient

Practice problem step 1-3 Recognize it is a vapor fugacity problem Recognize it is for a mixed system Recognize I want EOS (not correlation tables)

Practice problem – step 4 Choose the CORRECT equation

Practice problem step 5 Convert to z, multiply by n and take the proper derivative Keep constants and n together

Practice problem step 6 Integrate and simplify

Practice problem step 6 Integrate and simplify

How does your book do it? Vo=nTRT/Plow Solve for fi Set limit of Plow  0 Solve for

Summary Recognize it is a vapor fugacity, whether it is a mixture or pure, and that I want you to use an EOS Based on the EOS, choose the right equation

Summary For mixtures first take the appropriate derivative Plug everything in, integrate, and simplify Let’s do some CW