Assume that the parameter b in Eq. (9.8-6):P=\frac{RT}{V_{m}-b} can be identified with the van derWaals parameter b. Calculate the radius of an argon atom from the value of the van der Waals parameter b in Table A.3.
| Table A.3 Parameters for Some Equations of State | ||
| Parameters for the van derWaals Equation of State | ||
| \Bigl(P+\frac{a}{V^{2}_{m}} \Bigr)(V_{m}-b)=RT ; P=\frac{RT}{V_{m}-b}-\frac{a}{V^{2}_{m}} | ||
| Substance | a/Pa m^{6} mol^{−2} | b×10^{5}/m^{3} mol^{−1} |
| Ammonia | 0.4225 | 3.707 |
| Argon | 0.1363 | 3.219 |
| Carbon dioxide | 0.3640 | 4.267 |
| Helium | 0.003457 | 2.370 |
| Hydrogen | 0.02476 | 2.661 |
| Methane | 0.2283 | 4.278 |
| Neon | 0.8636 | 1.709 |
| Nitrogen | 0.1408 | 3.913 |
| Oxygen | 0.1378 | 3.183 |
| Xenon | 0.4250 | 5.105 |
| Water | 0.5536 | 3.049 |
| Parameters for the Berthelot Equation of State | ||
| \Bigl(P+\frac{a}{TV^{2}_{m}} \Bigr)(V_{m}-b)=RT ; P=\frac{RT}{V_{m}-b}-\frac{a}{TV^{2}_{m}} | ||
| Substance | a/Pa m^{6} mol^{−2}K | b×10^{5}/m^{3} mol^{−1} |
| Ammonia | 171 | 3.70 |
| Argon | 20.5 | 3.20 |
| Carbon dioxide | 111 | 4.28 |
| Helium | 0.019 | 2.41 |
| Methane | 43.6 | 4.27 |
| Neon | 0.98 | 1.77 |
| Nitrogen | 17.3 | 3.87 |
| Oxygen | 21.3 | 3.18 |
| Xenon | 121 | 5.13 |
| Water | 357 | 3.04 |
| Parameters for the Dieterici Equation of State | ||
| Pe^{a/V_{m}RT(V_{m}-b)}=RT; P=\frac{RT}{V_{m}-b}e^{−a/V_{m}RT} | ||
| Substance | a/Pa m^{6} mol^{−2} | b×10^{5}/m^{3} mol^{−1} |
| Ammonia | 0.540 | 4.00 |
| Argon | 0.174 | 3.47 |
| Carbon dioxide | 0.468 | 4.63 |
| Helium | 0.0046 | 2.60 |
| Hydrogen | 0.031 | 2.83 |
| Methane | 0.293 | 4.62 |
| Neon | 0.028 | 1.91 |
| Nitrogen | 0.176 | 4.19 |
| Oxygen | 0.177 | 3.45 |
| Xenon | 0.536 | 5.56 |
| Water | 0.709 | 3.29 |
| Parameters for the Redlich-Kwong Equation of State | ||
| P=\frac{RT}{V_{m}-b}-\frac{a}{T^{1/2}V_{m}(V_{m}+b)} | ||
| Substance | a/Pa m^{6} mol^{−2} K^{1/2} | b×10^{5}/m^{3} mol^{−1} |
| Ammonia | 8.59 | 2.56 |
| Argon | 1.69 | 2.22 |
| Carbon dioxide | 6.44 | 2.96 |
| Helium | 0.00835 | 1.67 |
| Hydrogen | 0.14195 | 1.813 |
| Methane | 3.20 | 2.96 |
| Neon | 0.149 | 1.22 |
| Nitrogen | 1.56 | 2.68 |
| Oxygen | 1.74 | 2.21 |
| Xenon | 7.20 | 3.56 |
| Water | 14.24 | 2.11 |
| From R. C.Weast, ed., Handbook of Chemistry and Physics, 64th ed., CRC Press, Boca Raton, FL, 1983, p. D191. | ||
