Van der Waals Equation

Written by Jerry Ratzlaff on . Posted in Thermodynamics

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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

 

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Tags: Gas Equations Ideal Gas Equations