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# Arginine vasopressin is a pituitary hormone. It helps to 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 vasopressin in 100 mL of solution had an osmotic pressure of 3.70 mm Hg at 25$^{0}C$. What is the molecular weight of the hormone?

Last updated date: 20th Jun 2024
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Hint: Antidiuretic hormone also known as vasopressin is a hormone which is synthesized as a peptide prohormone in the neurons present in the hypothalamus and it gets converted into arginine vasopressin (AVP).

Given in the question:
Mass of vasopressin = 21.6 mg
Mass of vasopressin (w)= $(21.6)({{10}^{-3}})$ g
The volume of the solution is = 100 ml
Volume of the solution (V)= $\dfrac{100}{1000}$ liters
Osmotic pressure of the solution = 3.70 mm
Osmotic pressure of the solution ($\pi$) =$\dfrac{3.70}{760}$ atm
Temperature of the solution = 25 $^{0}C$
Temperature of the solution (T) = $25+273$= 298 K
Now we use have to find the molecular weight we will use the given formulae which gives a relation between all the given quantities:
$\pi V=\dfrac{w}{M}RT$
$(\dfrac{3.70}{760})(\dfrac{100}{1000})=(\dfrac{(21.6)({{10}^{-3}})}{M})(0.0821)(298)$
Hence, an aqueous solution containing 21.6 mg of vasopressin in 100 mL of solution had an osmotic pressure of 3.70 mm Hg at 25$^{0}C$the molecular weight of the hormone (M) = 1085 g/mol