Question

In textbook Engineering and Chemical Thermodynamics (2nd Edition), chapter 7 problem 33

7.33 A mixture of 2 moles propane (1), 3 moles butane (2), and 5 moles pentane (3) is contained at 30 bar and 200°C. The van der Waals constants for these species are: Species a3Jm3mol22 4 b3m3/mol4 Propane 0.94 9.06 3 1025 Butane 1.45 1.22 3 1024 Pentane 1.91 1.45 3 1024 Determine the fugacity and fugacity coeffi cient of propane using the following approximations: (a) the Lewis fugacity rule (b) the virial form of the van der Waals equation truncated to the second term.

Im unsure how to find partial molar volume here.

Answer 1

Ans. a) Here we are supposed to find the fugacity and fugacity coefficient of propane at 220 deg. C and 30 bar,

we will find the values for fugacity by Lewis fugacity rule

we know fugacity =f, can be given by Lewis fugacity rule as:

;

for this first we will calculate the fugacity coefficient by the standard virial equation.

b) Here P = is total given pressure, unit of fugacity will be same here as of pressure, since fugacity coefficient is a unitless quantity

For propane the standard values of critical temperature T_C and critical pressure P_c are:

and

Here given:

For propane we get the values for reduced temperature T_r and reduced pressure P_r as:

;

;

Now we will substitute in the following standard relations to get the fugacity cofficient as:

;................................................................................(a)

Here we will solve for B^o, by using the relation for propane using standard parameters as:

we know:

now substituting the value for T_r we get:

(these are unitless parameters)

Now we will find for B¹, by using the relation for propane using standard parameters as:

we know:

(these are unitless parameters)

now substituting the value for T_r we get:

(these are unitless parameters)

Now we will substitute in the values of  B¹ and  B^o, in equation (a) to find the fugacity coefficient of propane:

we have

Here fugacity coefficient is a unitless quantity, it is a ratio of fugacity to pressure

we get the fugacity coefficient of pressure for propane as: 0.59866

we will find the values for fugacity by Lewis fugacity rule

we know fugacity =f, can be given by Lewis fugacity rule as:

;

Here P = is total given pressure, unit of fugacity will be same here as of pressure, since fugacity coefficient is a unitless quantity

Hence we will get the value for fugacity of propane as:

we get the fugacity as 17.98 bar.

Note: we need not to calculate the partial molar volume here only to find the fugacity and fugacity coefficient of propane

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