Air is approximately 80% nitrogen and 20% oxygen (on a mole basis). If 6 g of hydrogen is added to a 22.4 liter maintained at 0 degrees c and initially filled with air at 1 atm pressure, what will be the molecular mass (i.e. the average molecular mass) of the hydrogen-air mixture to 3 sig figs?
I tried to use PV=nRT to get the number of moles
(1 atm*22.4 L)/(.08206*273 K)= .9998 mol
I multiplied it by 62.04 g/mol (mass of H2 + O2 + N2) and got 62.027 g, but I don't think this is right because I didn't incorporate the composition of air (80% nitrogen and 20% oxygen) into the problem. Could someone help me out?
Ok, here goes:
Change the percents to a mass basis>
.80*molmassN2 + .20*molmassO2= mass air inside.
Figure the mass of the air inside.
Now add the mass of H2.
Now you have the original air, plus H2.
You have .8 mole N2, .2moleO2, and 6/molmassH2. That is about 4 moles of the mixture total.
Take the total mass inside
.8 *molmassN2 +.2molmassO2 + 6/molmassH2
divide by the total "moles" inside (about 4).
That is the "average" mole mass, whatever that means. This reminds me of taking a class of 10 boys and 10 girls, and using statistics to find the average gender.
But, average "mol" mass has some uses.
To calculate the molecular mass of the hydrogen-air mixture, you need to take into account the composition of air and the mass of hydrogen added. Here are the steps you can follow:
1. Determine the mass of air inside the container initially.
- The composition of air is approximately 80% nitrogen and 20% oxygen.
- Let's assume the total mass of air inside the container is "M".
- The mass of nitrogen in air is 0.8 * M, and the mass of oxygen is 0.2 * M.
2. Add the mass of hydrogen to the total mass of air.
- The total mass of air inside the container plus the mass of hydrogen is (0.8 * M) + (0.2 * M) + 6 g.
- This is because you are adding 6 g of hydrogen, which does not affect the mass of nitrogen and oxygen since they were already present inside the container.
3. Calculate the total number of moles of the mixture.
- Convert the total volume of the container to moles using the ideal gas law:
(1 atm * 22.4 L) / (0.08206 * 273 K) = approximately 0.9998 mol
- This is the total number of moles of the mixture inside the container.
4. Calculate the average molecular mass of the mixture.
- Divide the total mass of the mixture (from step 2) by the total number of moles (from step 3).
- This will give you the average molecular mass of the hydrogen-air mixture.
It is worth noting that the average molecular mass is the weighted average of the molecular masses of the components, considering their proportions in the mixture.