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Homework Help: Hydrostatic pressure

  1. Feb 25, 2007 #1
    Hi

    I am to calculate the hydrostatic pressure difference - given by the

    \Delta P = n*f/A

    where f = 0.4 kcal/mol/Å. The unit cell has the dimension 23Å x 19.9Å x 30.4 Å and the number of water molecules are 5.4 Å in the z-direction with a molar volume of 55.5 mol/l.

    I start by calculating the moles of water
    n = 23Å*19.9Å*5.4Å*55.5 mol/l 1000 l/Å^3 = 1.37*10^-19 mol

    Than I assume that the force is acting on the 5.4Å depth of water which gives a pressure of

    \Delta P = 5.4Å*0.4 kcal/mol/Å*1.37*10^-19 mol /(23*10^-10*19.9*10¯10)m² = 6.47*10^-18 kcal/m^2

    It seems a little strange and how to convert into Pascal? Any help or comments appreciated. Thanks in advance
     
  2. jcsd
  3. Feb 25, 2007 #2

    Gokul43201

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    1. Homework & Coursework is the correct place for this question (not the Chemistry subforum).

    2. What is the context for all this?

    3. Why have you substituted the depth, d=5.4A into the equation?

    4. Once you make the correction in 3, you will find you have the correct dimensions to convert to units of Pa.
     
  4. Feb 25, 2007 #3
    so this should be okay

    0.4 kcal/mol/Å*1.37*10^-19 mol /(23*10^-10*19.9*10¯10)m² = 1.1988e-08 kcal/Å /m^2

    and than convert this to Pa? Thanks in advance
     
  5. Feb 25, 2007 #4

    Gokul43201

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    I can't attest to the correctness of the calculation without knowing what the question is, but now it is at least dimensionally correct.
     
  6. Feb 28, 2007 #5
    Hi

    Sorry if it is bit unclear.

    I should calculate the pressure difference with a nanotube and on water on both sides. So I will use the formula \Delta P = n*f/A where f = 0.4 kcal/mol/Å and the unit cell of the system is 23Å*19.9Å*30.4Å and the number of water is in the 5.4 Å thick layer with a molar volume of 55.5 mol/l. So I end up with this

    \Delta P = 10^10 Å/m 0.4 kcal/mol/Å*1.37*10^-19 mol /(23*10^-10*19.9*10¯10)m² = 119.88 kcal/m m^2

    which I convert to MPascal with 1 kcal/m = 4184 N

    4184 m/kcal N * 119.88 kcal/m m^2 / 10^6 = 0.50 MPa

    Does this seems correct? Thanks in advance
     
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