Final answer:
To find the molar mass of hemoglobin, we must use the ideal gas law to determine the moles of oxygen and then the moles of hemoglobin from the given mass. The molar mass calculation suggests a higher molar mass than the answer choices suggest, implying an error in the data given.
Step-by-step explanation:
To determine the molar mass of hemoglobin, first, we need to use the provided conditions (1.53 mL of O2 at 37 °C and 743 torr) to find the number of moles of oxygen that react with hemoglobin. We can then apply these findings to figure out the number of moles of hemoglobin. Finally, we will calculate the molar mass of the hemoglobin using the mass given (1.0 g) and the mole amount computed.
The problem states that 1.0 g of hemoglobin can bind with four molecules of oxygen. Since the molar mass is the mass of one mole of a substance, and we have the mass of hemoglobin that combines with oxygen, we can use the ideal gas law and the stoichiometry relation between oxygen and hemoglobin to find the mole quantity.
The ideal gas law (PV=nRT) allows us to calculate the number of moles of oxygen (given that R = 0.0821 L·atm/mol·K and 1 atm = 760 torr), and once we have the moles of oxygen, we use the 4:1 ratio to find the moles of hemoglobin. With the number of moles of hemoglobin and the mass, we can calculate molar mass:
Molar mass = mass of hemoglobin / number of moles of hemoglobin
When we follow these calculations, it turns out that the molar mass of hemoglobin would be much higher than any of the answer choices provided, indicating that the question might have an error in the data presented (10.0 g of hemoglobin yields 6.2 × 104 g/mol in the reference provided, which is not consistent with typical values of hemoglobin molar mass and is much larger than answer choice d, 256 g/mol).