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19 May, 16:48

The osmotic pressure of a solution containing 5.87 mg of an unkonw protein per 10 ml of solution is 2.45 torr at 25 degree clesius. Find the molar mass of the unknown protein. 1 atm

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  1. 19 May, 17:25
    0
    The molar mass of the protein is 4453.7 g/mol

    Explanation:

    Step 1: data given

    Mass of the unknown protein = 5.87 mg = 0.00587 grams

    volume = 10 mL

    Osmotic pressure = 2.45 torr

    Temperature = 25.0 °C

    Step 2 = Calculate concentration

    π = i*M*R*T

    ⇒ π = the osmotic pressure = 2.45 torr = 2.45 / 760 atm = 0.003223684 atm

    ⇒ i = the van't Hoff factor = 1

    ⇒ M = the concentration =

    ⇒ R = the gas constant = 0.08206 L*atm/mol*K

    ⇒T = the temperature = 25.0 °C = 298 K

    0.003223684 = 1 * M * 0.08206 * 298

    M = 0.0001318 M

    Step 3: Calculate moles

    Moles = molarity * volume

    Moles = 0.0001318 M * 0.01 L

    Moles = 0.000001318 moles

    Step 4: Calculate molar mass

    Molar mass = mass / moles

    Molar mass = 0.00587 grams / 0.000001318 moles

    Molar mass = 4453.7 g/mol

    The molar mass of the protein is 4453.7 g/mol
  2. 19 May, 20:21
    0
    14.35g/mol

    Explanation:

    Using the osmotic pressure formula we can calculate the concentration of the unknown protein solution as follows:

    Π = iMRT

    Π = 2.45 torr

    Recall:

    760torr = 1atm

    2.45torr = 2.45/760 = 0.00322atm

    i = 1

    R = 0.082atm. L/K / mol

    T = 25°C = 25 + 273 = 298K

    M = ?

    M = Π / iRT

    M = 0.00322 / (1 x 0.082 x 298)

    M = 1.318x10^-4M

    Using the ideal gas equation (PV = nRT), let us find the number of mole as follows:

    V = 10mL = 10/1000 = 0.01L

    P = 1atm

    T = 25°C = 25 + 273 = 298K

    R = 0.082atm. L/K / mol

    n = ?

    PV = nRT

    n = PV / RT

    n = (1 x 0.01) / (0.082 x 298)

    n = 4.09x10^-4mol

    Now, we can find the molar mass of the unknown protein as follows:

    Mass of unknown protein = 5.87 mg = 5.87x10^-3g

    Number of mole of unknown protein = 4.09x10^-4mol

    Molar Mass of unknown protein = ?

    Number of mole = Mass / Molar Mass

    Molar Mass = Mass / number of mole of

    Molar Mass of unknown protein = 5.87x10^-3/4.09x10^-4 = 14.35g/mol
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