Raoults Law Again

Comparing this to Eq. 3.5, Raoult s law, we see that they are the same, except that Eq. 8.5 has a liquid-phase activity coefficient, while Raoult s law has set that equal to 1.0. Since we defined an ideal solution as one in which yj = 1.00 for all values of x we can see that Raoult s law is the ideal-solution simplification of the more general form shown in Eq. 8.5. From the fact that the calculated activity coefficients for acetone-water (Example 8.2) are greater than 1.00, we can see that this mixture is not an ideal solution and does not obey Raoult s law. 

Example 8.3 How much difference does nonideal solution behavior make in the acetone-water VLE To answer this, compute the boiling temperature and vapor composition that would correspond to a liquid with Xacetone = 0.05, if this were an ideal solution (7, = 1.00),—Raoult s law—and compare them to the experimental values. 

This is a repeat of Example 3.5. We must find, by trial and error, the temperature at which the sum of the computed ideal solution vapor-phase mol fractions is 1.00. For our first try, we guess r=80°C. Using the Antoine equation constants in Table A.2, we compute that at 80°C the two pure species vapor pressures for acetone and for water are 2.11 and 0.47 atm. Then multiplying each of these by the corresponding liquid mol fractions and dividing by 1 atm, we find that the computed vapor mol fractions are 0.106 and 0.444, and that their sum is 0.55. This is less than 1.00, so our assumed temperature is too low. These values are shown as the first data row in Table 8.A. The calculation was done on a spreadsheet, with which one can quickly repeat the calculation for various assumed temperatures and display the results in subsequent rows of Table 8. A. The assumed temperature that makes the sum of the vapor-phase mol fractions equal 1.00 is T = 96.406 °C. (We should not believe that we know any boiling temperature 0.001°C, we should report the calculated boiling temperature as 96.4°C).  

The choices of values for ff made here are often called Raoult s law type choices and the y, thus found are called Raoult s law-type activity coefficients. We can see why with Table 8.2. This formulation of simple, low-pressure VLE in terms of Raoult s law-type activity coefficients is the most commonly used formulation. When we see an activity coefficient for low-pressure VLE without a description of which type it is (i.e., what choices have been made 

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