# Van der Waals Equation

Written by Jerry Ratzlaff on . Posted in Thermodynamics

Van der Waals equation is a modification of the ideal gas law, corrects for the volume of, and attractive forces between gas molecules.

## Van der Waals Equation

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

### Where:

 Units 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 Constants Table

Material Molecular Formula ab
$$L^2 bar\;/\;mol^2$$$$L\;/\;mol$$
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 