Hemoglobin is a large molecule that carries oxygen in the body. An aqueous solution that contains 2.61 g of hemoglo- bin in 100.0 mL has an osmotic pressure of 7.52 mmHg at 25 °C. What is the molar mass of the hemoglobin? Assume hemoglobin does not dissociate in water. (LO 13.15) (a) 1.96 * 103 g>mol (b) 84.8 g/mol (c) 6.45 * 104 g>mol (d) 3.65 * 103 g>mol

Verified step by step guidance

1. Identify the formula for osmotic pressure: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor (which is 1 for non-dissociating solutes), \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
2. Convert the temperature from Celsius to Kelvin: \( T = 25 + 273.15 \).
3. Rearrange the osmotic pressure formula to solve for molarity \( M \): \( M = \frac{\Pi}{iRT} \).
4. Substitute the known values into the equation: \( \Pi = 7.52 \text{ mmHg} \), \( R = 0.0821 \text{ L atm/mol K} \) (convert mmHg to atm), and \( T \) in Kelvin.
5. Calculate the molar mass of hemoglobin using the formula: \( \text{Molar mass} = \frac{\text{mass of solute (g)}}{\text{moles of solute}} \), where moles of solute is \( M \times \text{volume in liters} \).

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 and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. In this context, determining the molar mass of hemoglobin involves using the mass of the solute and the volume of the solution to find the number of moles present, which can then be used to calculate the molar mass.

Ideal Solution Assumption

The ideal solution assumption posits that solute-solvent interactions are similar to solute-solute and solvent-solvent interactions, leading to predictable behavior in solutions. In this problem, it is assumed that hemoglobin does not dissociate in water, allowing for the use of the osmotic pressure equation without accounting for any changes in particle number due to dissociation, simplifying the calculation of molar mass.