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% w/w, % v/v, % w/v to mol/L

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  • % w/w, % v/v, % w/v to mol/L

    Hi there,
    I've been trying to solve this problem and just when I thought I had the solution, turns out I didn't.

    This is the problem:
    I have a bottle with 81% (v/v) of a liquid. 1 liter of the liquid weighs 1.305 kg. The molecular weight of the liquid is 89.9. What is the concentration in mol/L of this liquid?

    And then the same question for w/w and w/v instead of v/v.

    My thoughts:
    v/v: 0.81 liters per liter, so 0.81 * 1.305 = 1.06 kg per liter. 1060/89.9 = 11.76 moles/liter.
    w/v: 81 grams per 100 mL, so 810 grams per liter. 810/89.9 = 9.01 moles/liter.
    w/w: 81 grams per 100 grams, so 810 grams per kg, which means 810 grams per 0.77 liter, which gives 1060 grams per 1 liter. 1060/89.9 = 11.76 moles/liter.

    However, now I have the same solution for v/v and w/w, and I don't think that can be right... I feel like I'm missing some information in the problem, but it should be solveable...

    Any help would be greatly appreciated!

  • #2
    Re: % w/w, % v/v, % w/v to mol/L

    Originally posted by Unregistered View Post
    Hi there,
    I've been trying to solve this problem and just when I thought I had the solution, turns out I didn't.

    This is the problem:
    I have a bottle with 81% (v/v) of a liquid. 1 liter of the liquid weighs 1.305 kg. The molecular weight of the liquid is 89.9. What is the concentration in mol/L of this liquid?

    And then the same question for w/w and w/v instead of v/v.

    My thoughts:
    v/v: 0.81 liters per liter, so 0.81 * 1.305 = 1.06 kg per liter. 1060/89.9 = 11.76 moles/liter.
    w/v: 81 grams per 100 mL, so 810 grams per liter. 810/89.9 = 9.01 moles/liter.
    w/w: 81 grams per 100 grams, so 810 grams per kg, which means 810 grams per 0.77 liter, which gives 1060 grams per 1 liter. 1060/89.9 = 11.76 moles/liter.

    However, now I have the same solution for v/v and w/w, and I don't think that can be right... I feel like I'm missing some information in the problem, but it should be solveable...

    Any help would be greatly appreciated!
    You have to separately consider (and convert) what is in the numerator and denominator. Percent just adds confusion. What you have is 810 mL/L

    Now is density of the liquid of 1.305 kg/L the density of the pure liquid in the numerator or the mixture in the denominator? If the mixture, the only thing you have enough information for is to get a volume over weight percentage, which I have never seen used.

    If (and only if) the density of the numerator liquid (when pure) is 1.305 kg/L,then 0.81 L/L x 1.305 kg/L = 1.057 kg/L or 105.7 % w/v (the problem with w/v percentages is that they can exceed 100%, a little counter-intuitive.)
    1.057 kg/L x 1 mol/89.9 kg = 11.76 mol/L.

    If you want w/w percentage, you need two densities, the pure liquid in the numerator and the mixture (as mixed) in the denominator.

    Tip: It helps to label the substance as well as the units. I don't know what your liquid is but "810 mL of A/1 L of mixture" may help you keep track of what you've got and what densities, molecular weights, etc you need. Label them the same way. Check that not only are units cancelling correctly, but the substances align.

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    • #3
      Re: % w/w, % v/v, % w/v to mol/L

      Hi!

      Need help to solve this problem:

      Given: HCL 31.45% (w/v); S.G - 1.16; tank volume- 207.6L

      Required: Convert 75 g/L of HCL into % (v/v)

      Comment

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