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Hydrogen specific volume

  1. Sep 22, 2012 #1
    1. The problem statement, all variables and given/known data

    A sample of hydrogen is at a pressure of 1000mb and a temperature of +10° C.
    Calculate its specific volume.


    2. Relevant equations

    I'm guessing PV=mRT

    3. The attempt at a solution

    P=1 bar
    m=2 g
    R=constant (do I use the universal constant or is there a constant for Hydrogen? If so how do I find it)
    T=283.15K
     
    Last edited: Sep 22, 2012
  2. jcsd
  3. Sep 22, 2012 #2
    The ideal gas law is PV=nRT where n is number of gas moles. You can use the ideal gas law, but you first have to find how many moles of hydrogen are in 2kg of hydrogen. To do this, you can use this conversion factor for hydrogen:

    [itex]\displaystyle \frac{1.008 g}{mole}Hydrogen[/itex]
     
  4. Sep 22, 2012 #3
    Ok so I don't know why I typed 2kg of hydrogen. Its a sample of hydrogen which is 1 gram but since Hydrogen is H2 in the atmosphere it should be 2 grams which is 2 moles correct?
     
  5. Sep 22, 2012 #4
    If the problem states that it's a 1 gram sample of Hydrogen, then the mass is 1 gram. Hydrogen gas is indeed H2, which means each molecule contains two Hydrogen atoms. To account for this, you make a new conversion factor for H2, multiplying the mass of hydrogen by 2.

    [itex]\displaystyle \frac{2.016 g}{mole}H_2[/itex]
     
  6. Sep 22, 2012 #5
    Ok redid some work

    Density = (P * MW) / (R * T)
    0.9869231693139999 atm
    Molecular weight of 2 g/mol
    R = 0.08206 L*ATM / mol*K
    T = 283.15K

    1.97384/23.235289 = 0.08495 g/L

    specific volume = 1/density
    specific volume of hydrogen = 11.77163 g/L

    Maybe yes?
     
  7. Sep 22, 2012 #6
    It looks alright, but when you take 1/density at the end, the units change to L/g. However, there was no need to use the density equation. Allow me to show you a simpler way:

    [itex]\displaystyle 1g\: H_2 ×\frac{1\: mole}{2.016 g}=0.5\:mole\: H_2[/itex]

    [itex]\displaystyle PV=nRT[/itex]

    [itex]\displaystyle V=\frac{nRT}{P}[/itex]

    n is the number of moles of H2 (0.5), R is the gas constant, and T and P are given. This gives the volume of one gram of hydrogen gas, which is equal to the specific volume.
     
  8. Sep 22, 2012 #7
    Awesome, thanks for explaining an easier way too!
     
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