How many moles of air are in the tank?

In summary: V=nRT but it was giving me weird numbers for n.In summary, the problem is that the given information does not give enough information to solve for the pressure and volume of air in the tank.
  • #1
mawalker
53
0
I am having trouble setting up this problem. Especially part A of the problem. I think I have a good idea of what to do for part B, but could anyone give me any hints on how to find moles from the given information?


A 14.0 cm-diameter compressed-air tank is 40.0 cm tall. The pressure at 30.0 C is 150 atm.

A.

How many moles of air are in the tank?

B.

What volume would this air occupy at STP?
 
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  • #2
Do you know the ideal gas equation? That should be all you need for both parts.
 
  • #3
yes, pV = nRT... would the volume be 4/3 pi(7)^3*(40) = 57470.2 ?
 
  • #4
No, if it's a cylinder the volume is [itex]2\pi r^2 h[/itex].

[itex]\frac{4}{3}\pi r^3[/itex] is the volume of a sphere.
 
  • #5
thanks, i always get the volume equations mixed up. using pV=nRT i got 150 atmospheres(pressure)*12315.04L(Volume)= n * .08206 (gas constant) * 303 (temperature K)

which gave me 1847256 = 24.86n

solving for n i got n = 74293.86... this seems like a lot of moles...
 
  • #6
do i need to do an additional conversion to get volume into L?
 
  • #7
I'd just convert atmospheres into pascals 1atm = 1.01x10^5 Pa, and use the standard form of the gas constant.
 
  • #8
hmmm... that made it even worse... i took (15150000 pa)(12315.04 cm3) = n (8.3145) (303) solving for n gave me 74057610.2 ... this still seems like a lot of moles
 
  • #9
Your volume should be in m^3.
 
  • #10
Just noticed your volume is out by a factor of two anyway, since the volume of a cylinder is [tex]\pi r^2 h = \frac{\pi d^2 h}{4}[/tex]
 
  • #11
ahhh, I'm still getting a ton of moles... converting from cm^3 to m^3 i got 61.58 m^3...

so 15150000 pa (61.58 m^3) = 93286420

(8.3145) constant * 303 degrees K = 2519.29n

divide both sides by 2519.29

and i find that n = 370288
 
  • #12
1 cm^3 = (1/100)^3 m^3 = 1E-06 m^3
 
  • #13
ahhh, thank you...that was the problem... ok now I'm having a little bit of trouble with part B. it asks how much volume it would occupy at stp

at stp i know:
T= 0 C or 273 K
P=1 atm or 1.01 *10^5 pa

so using pV=nRt

(1.01*10^5)V = (37.1 mol)(273 K)(8.3145 constant)

solving for V i get 3.08 m3 and this answer is not correct. i don't see what i am doing wrong here.
 
  • #14
Isn't standard pressure 1bar, i.e. 1x10^5 Pa not that it makes a difference.
Rearrange the equation before you put the numbers is in it makes it much easier. V = nRT / P, I assume you're making some silly mistake because the numbers look correct.
 
  • #15
thanks, it was a silly error...
 

Related to How many moles of air are in the tank?

1. How is the number of moles of air in a tank calculated?

The number of moles of air in a tank can be calculated by dividing the total volume of the tank by the molar volume of air at the given temperature and pressure. The molar volume of air is approximately 22.4 L/mol at standard temperature and pressure (STP).

2. What is the molar volume of air at STP?

The molar volume of air at standard temperature and pressure (STP) is approximately 22.4 L/mol. This means that 22.4 liters of air at STP contain one mole of air molecules.

3. How do I convert the number of moles of air to the mass of air in the tank?

To convert the number of moles of air to the mass of air in the tank, you will need to know the molar mass of air. The molar mass of air is approximately 28.97 g/mol. Multiply the number of moles of air by the molar mass to get the mass of air in grams.

4. Does the temperature and pressure of the air in the tank affect the number of moles of air?

Yes, the temperature and pressure of the air in the tank will affect the number of moles of air. This is because the molar volume of air is dependent on temperature and pressure. At higher temperatures and pressures, the molar volume of air will be larger, resulting in a higher number of moles of air in the tank.

5. Can the number of moles of air in a tank change over time?

Yes, the number of moles of air in a tank can change over time. This can happen due to changes in temperature and pressure, as well as the addition or removal of air from the tank. However, if the temperature and pressure remain constant and there is no addition or removal of air, the number of moles of air will remain the same.

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