What is the molecular mass of met-enkephalin if 20.0mL of an aqueous solution containing 15.0 mg met-enkephalin at 298 K supports a column of water 32.9 cm high? The density of mercury at 298K is 13.534 g/mL.

The molar mass of met-enkephalin is 573 g/mol

Explanation:

Step 1: data given

Volume of the aqueous solution = 20.0 mL = 0.02 L

Mass of met-enkephalin = 15.0 mg = 0.015 grams

Temperature = 298 K

Water column is 32.9 cm high

The density of mercury at 298K is 13.534 g/mL

Step 2: The osmotic pressure

P = cRT

⇒ with P = the osmotic pressure

⇒ with c is the concentration in mol/L

⇒ with R is the gas constant (L. atm/mol. K)

⇒with T the temperature (K)

if the water column is 32.9 cm = 32.9/13.534 mmHg. = 0.032 atm

⇒ Pressure = 0.032 atm

⇒ 0.032 atm = c * 0.08206 L*Atm/K*mol

⇒ T = t the temperature = 298 K

c = P / RT

c = 0.032atm / (0.08206*298)

c = 0.00131 M

Step 3: Calculate moles

Moles = Molarity * volume

Moles = 0.00131 M * 0.020 L

Moles = 0.0000262 moles

Step 4: Calculate molar mass

Molar mass = mass / moles

Molar mass = 0.015 grams / 0.000026 moles

Molar mass = 573 g/mol

The molar mass of met-enkephalin is 573 g/mol