Thousands of buses run on compressed natural gas (CNG) to reduce pollution and t

Question

Thousands of buses run on compressed natural gas (CNG) to reduce pollution and to save on fuel costs. CNG, which is mostly methane, is stored on the roofs of the buses in large tanks under high pressure. If the density of CH_4 in a tank at 25 degree C is 155g/L, use (a) the van der Waals equation and (b) the ideal gas equation to calculate the methane gas pressure. (a) van der Waals Did you calculate n, the number of moles of CH_4, correctly? Did you convert the temperature to Kelvin? What volume did you use in your calculation? Did you use the correct value of R? Did you use the correct values of a and b? Did you include both terms in the van der Waals equation? Did you check your math and units carefully? (b) ideal gas law

Explanation / Answer

Vanderwall equation of state is given by

(P+n2a/V2)*(V-nb)= nRT, n =moles= mass/Molecular weight = m/W, V= Volume in L, P =pressure in bar, a=2.283 L.bar/mol2, b= 0.4278 L/mol R =8.314/100 =0.08314 L.bar/mole.K

(P+n2a/V2)= nRT/(V-nb)

P= (nRT/(V-nb) – n2a/V2

If d = density = mass/ Volume= m/V

P= (m/w)*RT/ (V*(1-(n/V*b)) – n2a/V2

    =(d/W)*RT/ (1-d/wb)- d2/ W2a

For CH4, vanderwalll constants are, a= 2.283 L2bar/Mol2 and b= 0.04278 L/mol

P= (155/16)*0.08314 L.bar/mole. K *298.15/ (1-155*0.04278/16) – 155*155*2.283/ 16*16 =324 bar =324*0.9869 atm=320 atm

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