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24 October, 06:43

If the vapor pressure of an aqueous solution containing 6.00 moles of a nonvolatile solute has a vapor pressure of 19.8 torr, and given that the vapor pressure of water at room temperature is 23.7 torr, how many total moles are present in solution? Your answer should have three significant figures.

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  1. 24 October, 06:59
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    36.5 mol

    Explanation:

    The vapor pressure of a solution of a non volatile solute in water is given by Raoult's law:

    P H₂O = χ H₂O x P⁰ H₂O

    where χ H₂O is the mole fraction of water in the solution and P⁰ H₂O

    In the turn the mole fraction is given by

    χ H₂O = mol H₂O / total # moles = mol H₂O / ntot

    Thus

    P H₂O = mole H₂O / n tot x P⁰ H₂0

    now the mol of H₂O is equal n tot - 6 mol solute

    Plugging the values given in the question and solving the resultant equation

    19.8 torr = (ntot - 6) x 23.7 torr / n tot

    19.8 ntot = 23.7 ntot - 142.2

    ntot = 36.5 (rounded to 3 significant figures)
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