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21 August, 20:43

A 226 mL solution containing 22 g of a protein in toluene has an osmotic pressure of 0.053 atm at 27 oC. What is the molar mass (in g/mol) of the protein

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  1. 21 August, 20:57
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    4.4 * 10⁴ g/mol

    Explanation:

    The osmotic pressure (π) is a colligative property that can be calculated using the following expression.

    π = M * R * T

    where,

    M: molarity

    R: ideal gas constant

    T: absolute temperature (27°C + 273.15 = 300 K)

    Let's use it to find the molarity of the protein.

    M = π / R * T

    M = 0.053 atm / (0.082 atm. L/mol. K) * 300 K

    M = 2.2 * 10⁻³ M

    The molarity of the protein is:

    M = mass of the protein / molar mass of the protein * liters of solution

    molar mass of the protein = mass of the protein / M * liters of solution

    molar mass of the protein = 22 g / 2.2 * 10⁻³ mol/L * 0.226 L

    molar mass of the protein = 4.4 * 10⁴ g/mol
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