Arginine vasopressin is a pituitary hormone. It helps regulate the amount of water in the blood by reducing the flow of urine from the kidneys. An aqueous solution containing 21.6 mg of vasopressinin 100.0 mL of solution has an osmotic pressure at 25 ¢ªC of 3.70 mmHg. What is the molecular mass of the hormone?
To determine the molecular mass of arginine vasopressin, we can use the equation for osmotic pressure:
π = (n/V)RT
Where:
π = osmotic pressure
n = number of moles of the solute
V = volume of the solution in liters
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
First, let's convert the osmotic pressure from mmHg to atm:
3.70 mmHg * (1 atm/760 mmHg) = 0.0048684 atm
Now, let's rearrange the equation to solve for the number of moles of the solute (n):
n = (π * V) / (RT)
Given:
π = 0.0048684 atm
V = 100 mL = 0.1 L
R = 0.0821 L·atm/(mol·K)
T = 25 ¢ªC = 25 + 273.15 K = 298.15 K
n = (0.0048684 atm * 0.1 L) / (0.0821 L·atm/(mol·K) * 298.15 K)
n ≈ 0.0005956 mol
Finally, we can calculate the molecular mass (M) of arginine vasopressin using the equation:
M = molar mass / number of moles
Given:
molar mass = ?
number of moles = 0.0005956 mol
M = molar mass / 0.0005956 mol
To find the molar mass, we need to know the number of grams of vasopressin present in the solution (mass). However, the given information only provides the mass in mg (milligrams). We need to convert this to grams by dividing by 1000:
mass = 21.6 mg / 1000 = 0.0216 g
Now we can plug this into the equation to find the molecular mass:
M = 0.0216 g / 0.0005956 mol
M ≈ 36,300 g/mol
Therefore, the molecular mass of arginine vasopressin is approximately 36,300 g/mol.