[Charles CL]

Dear All,

1. The problem statement, all variables and given/known data
    At first i using percentage of composition of the gas molecular to calculate the density of the biogas.
    Molecular weight:
      1. CH4 = 16.0426,
      2. CO2 = 44.009
      3. O2 = 31.998
 
    Density:
      1. CH4 = 16.0426/22.4 = 0.7162 g/L
      2. CO2 = 44.009/22.4 = 1.9647 g/L
      3. O2 = 31.998/22.4 = 1.4285 g/L

    Composition:
      1. CH4 = 60%,
      2. CO2 = 38.5%
      3. O2 = 1.5%
 
Therefore,
    Actual Density:
      1. CH4 = 0.7162*60%
      2. CO2 = 1.9647*38.5%
      3. O2 = 1.4285*1.5%   
Total = 1.207545 g/L

However, this density is not based on parameter such as temperature.

2. Relevant equations

The following is the formula that i found to have temperature as parameter.
PV = znRT

3. The attempt at a solution

I have to stick with the density that i calculated earlier or should i calculate it based on the equation that i showed or perhaps there is other equation can precisely calculate the density of the biogas?

[billnotgatez]

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[Charles CL]

You have to show your attempts or thoughts at solving the question to receive help.
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Question has been corrected to show my attempt to get the answer.
Thanks.

[Borek]

    Density:
      1. CH4 = 16.0426/22.4 = 0.7162 g/L

You indirectly used the temperature here - 22.4 L is a molar volume of an ideal gas at 0°C. You can use PV=nRT to calculate the molar volume at any other temperature, and start from there.

[Charles CL]

Dear Borek,

P=30 mbar, T = 308 K
let n = 1 (i'm not sure how to calculate or get this number),
V = 0.854035

Molecular weight for gas, M = 126.1304 g/mol
PV=nRT,
V = 0.854035 m3

density = M/V
density = 147.69 g/m3.mol
However, this number is huge different from the typical of 1.2 kg/m3

[Borek]

P=30 mbar, T = 308 K

OK, although I don't know where you got 30 mbar from. Perhaps it is a partial pressure of something?

let n = 1 (i'm not sure how to calculate or get this number),

just an assumption, you could assume any other number of moles, in the end it will cancel out leaving exactly the same result.

V = 0.854035

OK

Molecular weight for gas, M = 126.1304 g/mol

No idea where you got it from.

density = M/V
density = 147.69 g/m3.mol

Correctly calculated from the above (questionable) number.

However, this number is huge different from the typical of 1.2 kg/m3

30 mbar is about 3% of the normal pressure, nothing surprising that the density is order of magnitude lower than that of a normal air at sea level.

[subro]

If the composition is in percentage by volume (and not by mass) and considering ideal gas, you can calculate the mean MW

0.6*16.0426+0.385*44.009+0.015*31.998=27.05 g/mol It differs significantly from 126.1304 g/mol

If it's in percentage by mass you can use the densities to get it. Anyway, it can't be above 44 g/mol