Final answer:
The osmotic pressure of a solution containing 19.95 mg of hemoglobin in 14.9 mL at 34°C is calculated to be 5.2215×10⁴ atm, using the formula Π = iMRT and the given molar mass.
Step-by-step explanation:
The subject of this question is the calculation of osmotic pressure in a solution using hemoglobin. To calculate the osmotic pressure, we can use the formula Π = iMRT, where Π is the osmotic pressure, i is the van 't Hoff factor (which is 1 for non-electrolytes like hemoglobin), M is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin. The molarity (M) is calculated by dividing the number of moles of solute by the volume of the solution in liters.
First, convert the mass of hemoglobin to moles using its molar mass and then find the molarity:
- Number of moles of hemoglobin = 19.95 mg × (1 g / 1000 mg) / (6.5×10⁴ g/mol) = 3.069×10⁵ mol
- Molarity (M) = 3.069×10⁵ mol / 0.0149 L = 2.06107×10⁴ M
Next, convert the temperature to Kelvin and plug in the values into the osmotic pressure formula:
- Temperature in Kelvin = 34°C + 273.15 = 307.15 K
- Osmotic Pressure (Π) = (1) × (2.06107×10⁴ M) × (0.0821 L×atm/mol×K) × (307.15 K)
- Osmotic Pressure (Π) = 5.2215×10⁴ atm
Thus, the osmotic pressure of the solution containing 19.95 mg of hemoglobin in 14.9 mL at 34°C is 5.2215×10⁴ atm.