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Thermodynamics, osmotic pressure

  1. Jul 20, 2013 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    I'm following the book of Reichl in thermodynamics at page 74 for osmotic pressure.
    I understand more or less what he's doing and how he reaches that the osmotic pressure is worth ##\pi =\frac{n_sRT}{V}## where ##n_s## is the number of moles of the dissolved substance, V is the volume of the solution (which is approximately worth the volume of water of the water+dissolved substance solution). I think I also understand the osmotic pressure physically. For example take a blood cell and suppose that in its interior it has salt (NaCl) dissolved in a water such that the concentration of salt is low. Suppose that the blood cell is immerged in water and that its membrane is permeable to water but not salt. Since the chemical potentials of water around the cell and inside the cell must be equal, this means that there will be more pressure pushing the membrane from the inside (due to the salt) than the water does from the outside. This difference of pressure would be the osmotic pressure.

    So I have a problem that I can't seem to solve because I don't have any information on the volume. Here it comes: A small bag made of a membrane permeable to water but not salt (NaCl) is filled with a solution with 1% by mass of salt in water and it is submerged into a water tank at 38°C; at a depth of 0.3 m.
    1)Calculate the osmotic pressure.
    2)What is the total pressure acting on the bag?
    Assume that the bag is small enough so that the water around it exerts a constant pressure.


    2. Relevant equations
    Already given.


    3. The attempt at a solution
    Part 1) :
    So I calculated that 1 mol of NaCl is worth 28g and 1 mol of H_2O is worth 18 g which makes that ##\frac{n_{\text{salt}}}{n_{\text{water}}}\approx 0.0064##.
    I tried to apply van't Hoff's law but I don't have any information on the volume of the bag.
    At first glance it looks like this information is hidden into the "1% concentration" sentence but I can't seem to extract the information.
    Any help is appreciated.

    Part 2) : Total pressure is simply the one due to depth (rho*g*h), minus the one due to osmotic pressure (since they act in opposite direction all over the membrane)
     
  2. jcsd
  3. Jul 21, 2013 #2

    SteamKing

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    Assume the bag is 1 liter, or 10 cc, or whatever small number you are comfortable with.
     
  4. Jul 21, 2013 #3

    fluidistic

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    Ahah! I didn't realize this could be arbitrary and still yields a good result! Thanks a lot.
    I reached an osmotic pressure of about ##9.19 \times 10 ^5 Pa##. While the pressure due to the depth of water is ##2940 Pa## and since they don't talk about any atmospheric pressure the total pressure on the bag is "huge".
     
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