Question

One molecule of hemoglobin will combine with four molecules of oxygen. If 1.0 g of hemoglobin combines with 1.53 mL of oxygen at body temperature (37 °C) and a pressure of 743 torr, what is the molar mass of hemoglobin?

Answer 1

The molar mass of hemoglobin is calculated by determining the number of moles of hemoglobin that reacts with oxygen using the ideal gas law, then using the mass of hemoglobin and the number of moles, applying the formula to find the molar mass.

Step-by-step explanation:

To calculate the molar mass of hemoglobin, we first need to establish the number of moles of oxygen that reacts with the given amount of hemoglobin. Since one molecule of hemoglobin combines with four molecules of oxygen, we can use the ideal gas law to determine the number of moles of oxygen: PV = nRT.

However, we need to adjust the pressure from torr to atm (1 atm = 760 torr) and the volume from mL to L (1000 mL = 1 L). After determining the number of moles of oxygen, we know that four times this amount will correspond to the number of moles of hemoglobin since it binds four oxygen molecules per hemoglobin molecule.

Finally, to calculate molar mass, we use the formula:

Molar mass = Mass of hemoglobin (g) / Number of moles of hemoglobin

In our example, the calculation would look something like this: If 10.0 g of hemoglobin corresponds to 1.6 × 10-4 moles, then the molar mass of hemoglobin is 10.0 g / (1.6 × 10-4 moles) = 6.2 × 104 g/mol.

Answer 2

The molar mass of hemoglobin is 217.4 g/mol.

Step-by-step explanation:

The molar mass of hemoglobin can be determined by using the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Rearranging the equation to solve for n gives us n = PV / RT. Given the pressure, volume, and temperature in the question, we can calculate the number of moles of oxygen that combine with 1.0 g of hemoglobin. Using the molar ratio of 4:1 between hemoglobin and oxygen, we can then calculate the molar mass of hemoglobin.

Using the given information:

Pressure (P) = 743 torr

Volume (V) = 1.53 mL

Temperature (T) = 37 °C = 310.15 K

The molar ratio of hemoglobin to oxygen = 1:4

Using the ideal gas law equation, n = PV / RT:

n = (743 torr * 1.53 mL) / (62.36 torr/mol·K * 310.15 K) = 0.0182 mol

Since one molecule of hemoglobin combines with four molecules of oxygen, the number of moles of hemoglobin is 0.0182 mol / 4 = 0.0046 mol.

Now, we can calculate the molar mass of hemoglobin by dividing the mass of hemoglobin (1.0 g) by the number of moles of hemoglobin:

Molar mass = 1.0 g / 0.0046 mol = 217.4 g/mol.