What osmotic pressure in mm Hg would you expect for an aqueous solution of 11.5 mg of insulin 1mol. weight = 59902 in 6.60 mL of solution at 298 K? What would the height of the water column be in meters? The density of mercury is 13.534 g/mL at 298 K.

Verified step by step guidance

1. Calculate the number of moles of insulin using the formula: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). Convert the mass of insulin from mg to g before substituting into the formula.
2. Calculate the molarity of the solution using the formula: \( \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \). Convert the volume from mL to liters.
3. Use the formula for osmotic pressure: \( \Pi = MRT \), where \( M \) is the molarity of the solution, \( R \) is the gas constant (0.0821 L atm K^{-1} mol^{-1}), and \( T \) is the temperature in Kelvin. Convert the osmotic pressure from atm to mm Hg by multiplying by 760 mm Hg/atm.
4. To find the height of the water column, use the formula: \( h = \frac{P}{\rho g} \), where \( P \) is the osmotic pressure in pascals, \( \rho \) is the density of mercury (convert g/mL to kg/m^3), and \( g \) is the acceleration due to gravity (approximately 9.81 m/s^2).
5. Convert the osmotic pressure from mm Hg to pascals (1 mm Hg = 133.322 Pa) before substituting into the formula for height.

Key Concepts

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution, as described by the formula π = iCRT, where π is osmotic pressure, i is the van 't Hoff factor, C is the molar concentration, R is the ideal gas constant, and T is the temperature in Kelvin.

Molarity and Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. To calculate the molarity of the insulin solution, one must first convert the mass of insulin into moles using its molar mass, then divide by the volume of the solution in liters. This concentration is essential for determining the osmotic pressure.

Hydrostatic Pressure and Height of Water Column

Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. The height of a water column can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height. In this context, the osmotic pressure calculated will be converted to the height of a mercury column using the density of mercury.