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

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

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