A gaseous mixture of carbon monoxide, carbon dioxide, methane and nitrogen gas i
ID: 1822301 • Letter: A
Question
A gaseous mixture of carbon monoxide, carbon dioxide, methane and nitrogen gas is analyzed with a gas chromatograph (GC). The output takes the form of a series of peaks where each peak corresponds to a component and a peak area (A) is proportional to the moles (n) of the component ( n = kA) in the sample injected in the GC. Area of carbon monoxide is 22, the area of methane is 42, the area of carbon dioxide is 28. The molar ratio of nitrogen to methane is known to be 0.26. Find the mole fraction and mass fraction of each component, and the average molecular weight of the mixture,Explanation / Answer
CO = 22k ; CH4 = 42k ; CO2 = 28k
N2 : CH4 = 0.26 -> N2 = 0.26*CH4 = 10.92k.
Mole Fraction be represented by X.
Total No. of Moles = (22+42+28+10.92)k = 102.92k
X(CO) = 22k/102.92k = 0.21375
X(CH4) = 42k/102.92k = 0.408
X(CO2) = 28k/102.92k = 0.272
X(N2) = 10.92k/102.92k = 0.1061
Mass of :
CO = 22k*28 = 616k
CH4 = 42k*16 = 672k
CO2 = 28k*44 = 1232k
N2 = 10.92k*28 = 305.76k
Total mass = 2825.76k
Let M denotes the mass fraction.
M(CO) = 0.218
M(CH4) = 0.238 [Use, Mass of component/Total mass]
M(CO2) = 0.436
M(N2) = 0.1082
Mol Wt.(Mix) = (X*Mol Wt.) ; [Summation of product of mole fraction and molecular weight of respective component]
= 27.4518.
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