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25 June, 23:41

In a study designed to prepare new gasoline-resistant coatings, a polymer chemist dissolves 6.143 g poly (vinyl alcohol) in enough water to make 100.0 mL of solution. At 25°C, the osmotic pressure of this solution is 0.272 atm. What is the molar mass of the polymer sample?

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  1. 26 June, 00:42
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    MM = 5,521.54 g/mol

    Explanation:

    To solve this, we need to use the expression for osmotic pressure which is the following:

    π = MRT (1)

    Where:

    M: Concentration of the solution

    R: gas constant (0.082 L atm / mol K

    T: temperature in K

    25 °C in Kelvin is: 25 + 273.15 = 298.15 K

    Now, we do not have the concentration of the solution, but we do have the mass. and the concentration can be expressed in terms of mass, molar mass and volume:

    Concentration (M) is:

    M = n/V (2)

    and n (moles) is:

    n = m/MM (3)

    Therefore, if we replace (2) and (3) in (1) we have:

    π = mRT/V*MM

    Solving for MM we have:

    MM = mRT/πV (4)

    All we have to do now, is replace the given data and we should get the value of the molar mass:

    MM = 6.143 * 0.082 * 298.15 / 0.1 * 0.272

    MM = 150.1859 / 0.0272

    MM = 5,521.54 g/mol

    This is the molar mass.
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