# 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?

Nov 13, 2015

$\text{65,000 g/mol}$

#### 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 $\text{1.00-g}$ sample.

So, the ideal gas law equation looks like this

$\textcolor{b l u e}{P V = n R T} \text{ }$, 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 $0.0821 \left(\text{atm" * "L")/("mol" * "K}\right)$
$T$ - 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 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 $n$, the number of moles of oxygen

$P V = n R T \implies n = \frac{P V}{R T}$

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 $\text{1.00 g}$ is the mass of $1.535 \cdot {10}^{- 6}$ 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 answer is rounded to two sig figs, the number of sig figs you have for the temperature of the oxygen gas.