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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

AVP has two important functions:

It increases the amount of solute free water which gets reabsorbed back into the circulation from the filtrate in the nephrons of the kidney tubules.

AVP will constrict the arterioles, which will eventually raise the pressure in the arteries. If the AVP gets released in high concentration then it will raise the blood pressure by inducing moderate vasoconstriction.

Some of the AVP get secreted directly to the brain from the hypothalamus and it plays an important role in social behavior. It is also responsible for the maternal response to stress and promotes heart muscles homeostasis.