Calculating Kilograms of Air in a 100m^3 Room | Molecular Weight of Air = 28g

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In summary, the conversation discusses the calculation of the amount of air contained in a box with specific dimensions at a given temperature and atmospheric pressure. After some initial confusion, it is determined that the correct answer is 115 kg of air.
  • #1
Bradracer18
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Here's the question:

How many kilograms of air are contained in a box 2.0m by 5.0m by 10.0m(at 1.0atm and 77 deg F)? Assume the molecular weight of air to be 28g.


This is what I've done so far, and can't come up with the correct answer.

77 deg F = 298 K
V=100m^3=100000 L
PV=nRT

(100000 L)/(298K * .0821 L*atm/mol*K) = 4087 moles

4087 moles / (28g/mole) = 146g or .146Kg air

What did I do wrong??

Thanks for the help fellas!

Brad
 
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  • #2
I don't see any errors. I think it might be time to call the answer you were given into question.
 
  • #3
Ok, thanks Tom. I couldn't find one either...he says you can write in your own answer if the multiple choice doesn't happen to show the correct answer...so I think that is what I shall do!

Thanks again,
Brad


***Edit...I found the problem...I took my 4087moles / 28g/mol...should have been 4087 x 28g/mol...to cancel units...and...what do you know...came up with the answer! lol...thanks again!
 
Last edited:
  • #4
Hoo boy, I can't believe I missed that. It's time for me to get some :zzz: :zzz: :zzz:
 
  • #5
lol...not a problem...I missed it too...lol...get some sleep!
 
  • #6
In converting the number of mol to grams, he needs to multiply (mol x g/mol) to get grams.

The value of R (I have) is 8.31 J/(mol K). I am also using an atmospheric
pressure of 101350 Pa.

n = p V/(R T) = 101350 (N/m^2) * 100 (m^3)
----------------------------
8.31 (N m/(mol K)) * 298 K

I get, n = 4093 mol.

4093 mol * 28 g/mol = 115 kg air in 100 m^3 room.
--------------------------
 

FAQ: Calculating Kilograms of Air in a 100m^3 Room | Molecular Weight of Air = 28g

1. How do you calculate the number of kilograms of air in a 100m^3 room?

To calculate the number of kilograms of air in a 100m^3 room, you first need to convert the volume from cubic meters to cubic centimeters by multiplying it by 1,000,000. In this case, 100m^3 would be equivalent to 100,000,000 cm^3. Then, you can use the ideal gas law (PV = nRT) to calculate the number of moles of air in the room, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature. Finally, multiply the number of moles by the molecular weight of air (28g) to get the mass in grams, and then convert it to kilograms by dividing by 1,000.

2. What is the molecular weight of air?

The molecular weight of air is approximately 28 grams per mole. This value is an average of the molecular weights of the two main components of air - nitrogen (N2) and oxygen (O2). The molecular weights of these gases are 28g/mol and 32g/mol, respectively, so the average molecular weight of air is 28g/mol.

3. How does the molecular weight of air affect its density?

The molecular weight of air does not directly affect its density. Density is determined by the mass of a substance and its volume. However, the molecular weight of air does affect its molar mass, which is the mass of one mole of a substance. This can indirectly affect the density of air, as a lower molar mass means more particles per unit volume and therefore a higher density.

4. Are there any other factors that can affect the number of kilograms of air in a 100m^3 room?

Yes, there are several factors that can affect the number of kilograms of air in a 100m^3 room. These include changes in temperature, pressure, and humidity. These factors can affect the density and molar mass of air, which in turn can affect the number of kilograms of air in a given volume.

5. How can this calculation be applied in real-life situations?

Calculating the number of kilograms of air in a given volume can be useful in various real-life situations. For example, in the field of HVAC (heating, ventilation, and air conditioning), this calculation can help determine the amount of air needed for proper ventilation in a room. It can also be used in air quality testing to measure the concentration of certain gases in a given space. Additionally, this calculation can be applied in industries such as aviation and scuba diving, where the amount of air in a given volume is crucial for safety and performance.

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