Assignment 2
CHY 381 Physical Chemistry 1

Predicting the vapour pressure of a substance from an equation of state
The vapour pressure is the pressure at which the liquid and vapour phases of a substance are in
equilibrium with each other. As you would expect, it is temperature dependent. For example,
pure water has a vapour pressure of 760 mm Hg (1.00 atm) at 100 °C: we call this the normal
boiling point. At lower temperatures, the vapour pressure decreases. For liquid water and
vapour to be in equilibrium at 25 °C, the pressure must be 23.8 mm Hg.

The vapour pressure at a particular temperature corresponds to the pressure value of the tie
line observed on an isothermal plot of p-Vm data. If we plot an equation of state, such as the
van der Waals EOS, we don’t observe a tie–line but can make one based on the Maxwell
construction: the tie–line divides the EOS curve into equal area regions, one above the tie–line
and one below. The ends of the tie–line correspond to the saturated liquid (lower value) and
vapour (higher value) molar volumes. In this assignment, you will use an accurate EOS to
calculate the vapour pressure and the saturated liquid and vapour molar volumes of propane,
C3H8, at 25 °C.
The Soave-Redlich-Kwong EOS is
𝑝𝑝= 𝑅𝑅𝑅𝑅
𝑉𝑉𝑚𝑚−𝑏𝑏− 𝑎𝑎[𝑅𝑅]
𝑉𝑉𝑚𝑚(𝑉𝑉𝑚𝑚 + 𝑏𝑏)
where
𝑎𝑎[𝑅𝑅] = 0.42748 �𝑅𝑅2𝑅𝑅𝑐𝑐2
𝑝𝑝𝑐𝑐 ��1 + 𝑘𝑘�1 −�𝑅𝑅 𝑅𝑅𝑐𝑐⁄ ��2
𝑘𝑘 = 0.480 + 1.574𝜔𝜔−0.176𝜔𝜔2
𝑏𝑏 = 0.08664𝑅𝑅𝑅𝑅𝑐𝑐
𝑝𝑝𝑐𝑐
and ω is the acentric factor for the gas: for propane, ω = 0.153. The critical temperature of
propane is 369.8 K and the critical pressure is 41.9 atm.

1. Use a spreadsheet program to calculate the pressure of propane according to Soave-
Redlich-Kwong EOS for molar volumes between 94 cm3 mol-1 and 2700 cm3 mol-1. Prepare
a p-Vm plot of the data. You should calculate 100 – 125 points and will need to vary the
intervals between Vm data points as the pressure changes more rapidly in some areas of the
range than others.

As in the previous assignment, it is critical to use fixed cells for constants and refer to them
rather than retyping the numbers in your formulas. It is quite easy to make mistakes in
entering the formulas and end up with an erroneous result. Here are three data points

(Vm/cm3mol-1, p/atm) you can use to check your work: (94, 48.495), (500, 17.500), (2700,
7.8264).
2. In the Maxwell construction, the tie-line at the vapour pressure pvap, extending from Vml
(liquid) to Vmv (vapour), splits the EOS into two equal area pieces – one above and one
below the tie line. When the EOS is integrated between the two molar volumes, the equal
areas cancel each other out and the integral becomes equal to the rectangular area given by
pvap (Vmv – Vml). This latter can be rearranged to give an expression pvap = (Vmv – Vml)-1 times
the integrated EOS. In order to save you substantial time and frustration, I’ve done this
integration and the complicated result is below. You will need to enter it into the
spreadsheet.
𝑝𝑝𝑣𝑣𝑣𝑣𝑣𝑣 = 1
𝑉𝑉𝑚𝑚𝑣𝑣−𝑉𝑉𝑚𝑚𝑙𝑙 �𝑅𝑅𝑅𝑅ln�𝑉𝑉𝑚𝑚𝑣𝑣−𝑏𝑏
𝑉𝑉𝑚𝑚𝑙𝑙 −𝑏𝑏�−𝑎𝑎
𝑏𝑏ln �𝑉𝑉𝑚𝑚𝑣𝑣(𝑉𝑉𝑚𝑚𝑙𝑙 + 𝑏𝑏)
(𝑉𝑉𝑚𝑚𝑣𝑣 + 𝑏𝑏)𝑉𝑉𝑚𝑚𝑙𝑙��

To determine the three unknowns, pvap, Vmv, and Vml, it is necessary to start with guesses for
the latter two parameters, estimated from a guess of the former. This can be done by eye,
using the plot from Q1. The pvap is calculated different three ways: by substitution of the
guessed Vmv into the EOS, by substitution of the guessed Vml into the EOS, and by calculation
of the equation with the integrated EOS above (which also requires the two molar
volumes). The three calculated pvap should all be the same number (but won’t be unless
your guesses are unbelievably good). We can compare the guesses by subtracting the

average of the three calculated pvap from each of the three calculated pvap. If we then sum
the squares of these differences, we have one “goodness of fit” parameter. We then use
the Solver routine to vary the values of the cells corresponding to the guessed Vmv and Vml,
changing them to make the value in the “goodness of fit” parameter cell as small as

possible. If we’re successful, we should end up with three very similar calculated pvap and
this and the contents of the cells corresponding to the Vmv and Vml values will be our
answers.

You need to hand in two files for this assignment: 1) the .xlsx spreadsheet you created and
used to calculate the values (it must be the spreadsheet, not a .pdf of the spreadsheet) and
2) a short document (no more than 1 page) with the p-Vm plot prepared in Q1 and the
values of pvap, Vmv and Vml determined using the solving process above. To check if your
answer is close to correct, the experimental Vmv is 2136 cm3 mol-1. You may be able to find
pvap with an online searc