Van der Waals Equation
Van der Waals equation is an equation of state that describes the behavior of real gases, taking into account the finite size of gas molecules and the attractive forces between them. It represents an improvement over the deal gas law, which assumes that gas molecules are point masses with no volume and no attractive forces between them.
The Van der Waals equation provides a more accurate description of the behavior of real gases, especially at high pressures and low temperatures, where the ideal gas law deviates from experimental observations. It takes into consideration the fact that gas molecules have both attractive and repulsive interactions, and that they occupy a finite volume, unlike the idealized point masses assumed in the ideal gas law.
- See Article Links - Peng-Robinson Equation of State, Peng-Robinson Equation of State, and Redlich-Kwong Equation of State
Van der Waals Equation |
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| \(\large{ \left[ p + a \; \left( \frac{n}{V}^2 \right) \right] \; \left( \frac{V}{n} - b \right) = R \; T }\) | ||
| Symbol | English | Metric |
| \(\large{ a }\) = correction for the intermolecular forces | \(\large{\frac{gal}{mol}}\) | \(\large{\frac{L}{mol}}\) |
| \(\large{ b }\) = adjusts for the volume occupied by the gas particles | \(\large{ft^3}\) | \(\large{m^3}\) |
| \(\large{ n }\) = number of moles of gas | \(\large{dimensionless}\) | |
| \(\large{ p }\) = pressure of gas | \(\large{\frac{lbf}{in^2}}\) | \(\large{Pa}\) |
| \(\large{ R }\) = specific gas constant (gas constant) | \(\large{\frac{ft-lbf}{lbm-R}}\) | \(\large{\frac{J}{kg-K}}\) |
| \(\large{ T }\) = temperature of gas | \(\large{F}\) | \(\large{K}\) |
| \(\large{ V }\) = volume of gas | \(\large{ft^3}\) | \(\large{m^3}\) |
Van der Waals Equation Constant |
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| Material | Moleculalar Formula | a \(\frac{L^2\; bar}{mol^2}\) | b \(\frac{L}{mol}\) |
| Acetylene | \(C_2 H_2\) | 4.516 | 0.0522 |
| Ammonia | \(NH_3\) | 4.225 | 0.03713 |
| Ammonium chloride | \(NH_4 Cl\) | 2.38 | 0.00734 |
| Benzene | \(C_6 H_6\) | 18.82 | 0.1193 |
| Bromine | \(Br_2\) | 9.75 | 0.05912 |
| Butane | \(C_4 H_{10}\) | 13.93 | 0.1168 |
| Carbon dioxide | \(CO_2\) | 3.658 | 0.04286 |
| Carbon disulphide | \(CS_2\) | 11.25 | 0.07262 |
| Carbon monoxide | \(CO\) | 1.472 | 0.03948 |
| Chlorine | \(Cl_2\) | 6.343 | 0.05422 |
| Decane | \(C_{10} H_{22}\) | 52.88 | 0.3051 |
| Ethanol | \(C_2 H_5 OH\) | 12.56 | 0.0871 |
| Ethyl acetate | \(C_4 H_8 O_2\) | 20.57 | 0.1401 |
| Ethylbenzene | \(C_8 H_{10}\) | 30.86 | 0.1782 |
| Ethylene | \(C_2 H_4\) | 4.612 | 0.05821 |
| Fluroethylene | \(C_2 H_3 F\) | 5.984 | 0.06504 |
| Fluorine | \(F_2\) | 1.171 | 0.02896 |
| Helium | \(He\) | 0.0346 | 0.0238 |
| Hydrogen | \(H_2\) | 0.2453 | 0.02651 |
| Hydrogen bromide | \(HBr\) | 4.5 | 0.04415 |
| Hydrogen chloride | \(HCI\) | 3.7 | 0.04061 |
| Hydrogen selenide | \(H_2 Se\) | 5.523 | 0.0479 |
| Hydrogen sulphide | \(H_2 S\) | 4.544 | 0.04339 |
| Isobutane | \(C_4 H_{10}\) | 13.36 | 0.1168 |
| Isobutylbenzene | \(C_{10} H_{14}\) | 40.4 | 0.2215 |
| Isobutyl acetate | \(C_6 H_{12} O_2 \) | 29.05 | 0.1845 |
| Mercury | \(Hg\) | 5.193 | 0.01057 |
| Methylamine | \(CH_3 NH_2\) | 7.106 | 0.05879 |
| Methyl propanoate | \(C_4 H_8 O_2\) | 20.51 | 0.1377 |
| Neopentane | \(C_5 H_{12}\) | 17.17 | 0.141 |
| Nitric oxide | \(NO\) | 1.46 | 0.0289 |
| Nitrogen | \(N_2\) | 1.37 | 0.0387 |
| Nitrogen dioxide | \(NO_2\) | 5.36 | 0.0443 |
| Nitrous oxide | \(N_2 O\) | 3.852 | 0.04435 |
| Octane | \(C_8 H_{18}\) | 37.86 | 0.2372 |
| Oxygen | \(O_2\) | 53.6 | 0.157 |
| Ozone | \(O_3\) | 3.57 | 0.0487 |
| Pentane | \(C_5 H_{12}\) | 19.13 | 0.1451 |
| Phosphorus | \(P\) | 53.6 | 0.157 |
| Propane | \(C_3 H_8\) | 9.385 | 0.09044 |
| Radon | \(Rn\) | 6.601 | 0.06239 |
| Silane | \(SiH_4\) | 4.38 | 0.0579 |
| Sulphur | \(S\) | 24.3 | 0.066 |
| Sulphur dioxide | \(SO_2\) | 6.865 | 0.05679 |
| Water | \(H_2 O\) | 5.537 | 0.03049 |
