# Van der Waals Equation

on . Posted in Thermodynamics

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.

## Van der Waals Equation

$$\large{ \left[ p + a \; \left( \frac{n}{V}^2 \right) \right] \; \left( \frac{V}{n} - b \right) = R \; T }$$
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

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 Tags: Gas Ideal Gas