# 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?

##### 1 Answer

#### Explanation:

The idea here is that you need to use the ideal gas law equation to determine how many *moles* of oxygen gas you have in that sample.

This will allow you to determine how many *moles* of hemoglobin you have in that

So, the ideal gas law equation looks like this

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

*universal gas constant*, usually given as

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,

This means that you will have to convert the volume from *mililiters* to *liters*, the temperature from *degrees Celsius* to *Kelvin*, and the pressure from *kilopascals* to *Pascals*.

Rearrange the ideal gas law equation and solve for

#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"#

You know that you need **one** hemoglobin molecule to bind with **four** oxygen molecules. This is equivalent to saying that **one mole** of hemoglobin will bind with **four moles** of oxygen gas.

This means that the amount of oxygen gas you have will need

#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 *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 answer is rounded to two sig figs, the number of sig figs you have for the temperature of the oxygen gas.