Factor a in Van der Waals equation of state off by a factor of 0.1?

In summary, the speaker is discussing their lab exam on the Joule-Thomson effect and using the Van der Waals equation of state for nitrogen and carbon dioxide. They have found that while the value for b is correct, the value for a is off by a factor of 0.1. They have compared their calculations to values from Wikipedia and Zemansky and Dittman, but are unable to determine the source of the discrepancy.
  • #1
dingo_d
211
0
Hello

So I have a lab exam in Joule-Thomson effect and I have given values for a and b for VdW equation of state for nitrogen and carbon dioxide. When I take the critical temp. and pressure and put it in the equations:

[tex]a=\frac{27(T_c R)^2}{64 p_c}[/tex] and
[tex]b=\frac{T_c}{8p_c}[/tex]

b gives correct value, but a is off by a factor of 0.1.

E.g. For [tex]CO_2[/tex], given in the table (the experiments and the Phywe can't be wrong) [tex]a=3.60 Pa\ m^6\ mol^{-2}[/tex], and if I put the values from the http://en.wikipedia.org/wiki/Critical_properties" on wikipedia, I get: [tex]a=3.60\times 10^{-1}\ Pa\ m^6\ mol^{-2}[/tex]. Not only for carbon dioxide, but for nitrogen too...

What is even weirder is that b is correct for the same temps and pressure!

So can someone find where this comes from? I calculated from Zemansky and Dittman the coefficients a and b and they are fine (the same as in wikipedia).

I converted all the necessary values (atm in Pa, used temp in K)...
 
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  • #2
The 0.36 is correct and the 3.6 is incorrect.
 

1. What is the purpose of the "a" factor in the Van der Waals equation of state?

The "a" factor in the Van der Waals equation of state represents the intermolecular forces between gas molecules. It takes into account the attraction between molecules, which causes them to deviate from ideal behavior.

2. Why is the "a" factor sometimes off by a factor of 0.1 in the Van der Waals equation of state?

The "a" factor is a constant value that is specific to each gas and is typically determined experimentally. However, due to variations in experimental conditions and measurement errors, the calculated "a" factor may sometimes be off by a small factor, such as 0.1.

3. How does an incorrect "a" factor affect the accuracy of the Van der Waals equation of state?

An incorrect "a" factor can significantly affect the accuracy of the Van der Waals equation of state. If the "a" factor is too high, the calculated pressure and volume values will be lower than the actual values, leading to underestimation of the deviation from ideal behavior. If the "a" factor is too low, the opposite will occur.

4. Can the "a" factor be adjusted to improve the accuracy of the Van der Waals equation of state?

Yes, the "a" factor can be adjusted to improve the accuracy of the Van der Waals equation of state. This can be done by comparing the calculated values with experimental data and adjusting the "a" factor until the two values match.

5. Are there any limitations to using the Van der Waals equation of state with an "a" factor that is off by 0.1?

Yes, there are limitations to using the Van der Waals equation of state with an "a" factor that is off by 0.1. While it may still provide a reasonable approximation, it may not accurately capture the behavior of the gas under certain conditions. In these cases, a more accurate "a" factor should be used or an alternative equation of state should be considered.

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