Calculation of Height of Water Column Due to Osmotic Pressure of Insulin Solution

Given data:
- Osmotic pressure of insulin solution at 298K = 0.0072 atm
- Density of Hg = 13.6 g/ml

To calculate the height of water column due to this pressure, we need to use the formula for calculating osmotic pressure:

π = MRT

where π is the osmotic pressure, M is the molar concentration of solute, R is the gas constant, and T is the temperature in Kelvin.

1. Calculation of Molar Concentration of Insulin Solution

To calculate the molar concentration of insulin solution, we need to use the molecular weight of insulin, which is 5808 g/mol.

Assuming that the insulin solution is dilute, we can use the following formula to calculate the molar concentration:

M = (ρsolute / Msolute) / ρsolvent

where ρsolute is the density of solute, Msolute is the molecular weight of solute, and ρsolvent is the density of solvent.

Assuming that the density of insulin solution is similar to the density of water, which is 1 g/ml, we get:

M = (1 g/ml / 5808 g/mol) / 1 g/ml = 1.72 x 10^-4 mol/L

2. Calculation of Height of Water Column

To calculate the height of water column, we need to use the following formula:

h = (π / ρg) / 10^5

where h is the height of water column in cm, π is the osmotic pressure in atm, ρ is the density of mercury in g/cm^3, and g is the acceleration due to gravity in cm/s^2.

Substituting the given values, we get:

h = (0.0072 atm / 13.6 g/ml) / 10^5 = 0.00053 cm

Therefore, the height of water column due to the osmotic pressure of insulin solution is approximately 0.00053 cm, which is equivalent to 0.053 mm or 53 microns.

Answer: 1. 0.76cm