Calculate the osmotic pressure of a solution containing 18.75 mg of hemoglobin in 15.0 mL of solution at 25 °C. The molar mass of hemoglobin is 6.5 x 10^4 g/mol.

Verified step by step guidance

1. Convert the mass of hemoglobin from milligrams to grams by dividing by 1000.
2. Calculate the number of moles of hemoglobin using the formula: $\text{moles}=\frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$.
3. Convert the volume of the solution from milliliters to liters by dividing by 1000.
4. Use the formula for osmotic pressure: $\mathrm{\Pi }=\frac{n}{V}RT$, where $n$ is the number of moles, $V$ is the volume in liters, $R$ is the ideal gas constant (0.0821 L·atm/mol·K), and $T$ is the temperature in Kelvin.
5. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

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.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is calculated by dividing the mass of the solute (in grams) by its molar mass (in g/mol) and then dividing by the volume of the solution (in liters). Understanding molarity is essential for determining how concentrated a solution is, which directly affects osmotic pressure.

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 atoms in a molecule. In this question, the molar mass of hemoglobin is crucial for converting the mass of hemoglobin present in the solution into moles, which is necessary for calculating the molarity and subsequently the osmotic pressure.