Each molecule of hemoglobin combines with four molecules of O2. If 1.00g hemoglobin combines with 1.60mL O2 at 37oC and 99.0 kPa, what is the molar mass of hemoglobin?

Question

Avery Adams · Accepted Answer

#"65,000 g/mol"#

The idea here is that you have to calculate the number of moles of oxygen gas in that sample using the ideal gas law equation.

This will allow you to determine how many moles of hemoglobin you have in that #"1.00-g"# sample.

Thus, this is how the ideal gas law equation appears.

#color(blue)(PV = nRT)" "#, where

#P# - the pressure of the gas #V# - the volume it occupies #n# - the number of moles of gas #R# - the universal gas constant, usually given as #0.0821("atm" * "L")/("mol" * "K")# #T# - the temperature of the gas, expressed in Kelvin

In order to be able to use this equation, you need to have the pressure, volume, and temperature of the sample expressed in the units used for the universal gas constant, #R#.

This means that the pressure will need to be converted from kilopascals to Pascals, the temperature from degrees Celsius to Kelvin, and the volume from mililiters to liters.

Rearrange the ideal gas law equation and solve for #n#, the number of moles of oxygen

#PV = nRT implies n = (PV)/(RT)#

#n = (99.0/101.325color(red)(cancel(color(black)("atm"))) * 1.60 * 10^(-3)color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 37)color(red)(cancel(color(black)("K")))) = 6.14 * 10^(-5)"moles"#

It is equivalent to saying that one mole of hemoglobin will bind with four moles of oxygen gas if you know that one hemoglobin molecule is needed to bind with four oxygen molecules.

Thus, the quantity of oxygen gas you possess will be required.

#6.14 * 10^(-5)color(red)(cancel(color(black)("moles O"_2))) * "1 mole hemoglobin"/(4color(red)(cancel(color(black)("moles O"_2)))) = 1.535 * 10^(-5)"moles of hemoglobin"#

Now, the molar mass of any substance tells you what the mass of one mole of that substance is. In your case, you know that #"1.00 g"# is the mass of #1.535 * 10^(-6)# moles, which means that one mole will have mass of

#"1.00 g"/(1.535 * 10^(-5)"moles") = 6.5 * 10^4"g/mol" ~~ color(green)("65,000 g/mol")#

The number of sig figs you have for the oxygen gas's temperature is the answer, which is rounded to two.

Cooper Anderson · Answer

undefined To find the molar mass of hemoglobin, we first need to calculate the number of moles of oxygen that combine with 1.00 g of hemoglobin. Then, we can use this information to find the molar mass of hemoglobin.

Given:
Mass of hemoglobin = 1.00 g
Volume of oxygen = 1.60 mL
Temperature = 37°C = 310 K (convert to Kelvin)
Pressure = 99.0 kPa

First, we convert the volume of oxygen to liters:
1.60 mL = 1.60 × 10^(-3) L

Next, we use the ideal gas law to calculate the number of moles of oxygen:
PV = nRT

Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)

Convert pressure to atm:
99.0 kPa = 0.976 atm

Now, substitute the values into the equation:
0.976 atm × 1.60 × 10^(-3) L = n × 0.0821 L·atm/mol·K × 310 K

Solve for n:
n ≈ 6.67 × 10^(-5) mol

Since each molecule of hemoglobin combines with four molecules of oxygen, the number of moles of hemoglobin is one-fourth of the number of moles of oxygen:
n_hemoglobin = (1/4) × n
n_hemoglobin ≈ (1/4) × 6.67 × 10^(-5) mol
n_hemoglobin ≈ 1.67 × 10^(-5) mol

Now, we use the definition of molar mass (mass/moles) to find the molar mass of hemoglobin:
Molar mass of hemoglobin = mass of hemoglobin / moles of hemoglobin
Molar mass of hemoglobin = 1.00 g / 1.67 × 10^(-5) mol
Molar mass of hemoglobin ≈ 5.99 × 10^(4) g/mol

Therefore, the molar mass of hemoglobin is approximately 5.99 × 10^(4) g/mol.