How many moles of gas are in the balloon?

  • Thread starter roam
  • Start date
  • #1
roam
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Homework Statement



A spherical balloon is inflated to a diameter of 36 cm. Assuming that the gas in the balloon is of atmospheric pressure (101.3 kPa) and is at a temperature of 20°C.

(a) How many moles of gas are in the balloon?

(b) If 21% of the molecules in the balloon are oxygen molecules, how many oxygen molecules are in the balloon?

The Attempt at a Solution



(a) I want to use the formula [tex]PV=nRT[/tex]

Volume is [tex]v=\frac{4}{3} \pi (0.18)^2 = 0.1357[/tex]

R is the constant 8.314

So [tex](101.3)(0.1357)=n8.314(20)[/tex]

Now if I solve for n I get [tex]n= {13.74}{166.28} = 0.082[/tex]

This is wrong because the correct answer must be 1.02. Do I need to convert the temprature to Kelvin/absolute temprature? ...because I tried that too & it didn't work.
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
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Given pressure is in kilopascal.
Temperature must be in Kelvin.
 
Last edited:
  • #3
mgb_phys
Science Advisor
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Temperature should be in kelvin
 
  • #4
rock.freak667
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Your temperature should be in Kelvin (K) and the pressure in Pa
 
  • #5
inutard
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Also, you squared your radii instead of cubing it.
 
  • #6
roam
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Okay 20 degrees is 293.15 in Kelvin, and I converted the pressure to pascals. So my equation becomes

[tex](101300)(0.1357)=n(8.314)(293.15)[/tex]

n= 5.64

But why is this still not the right answer? :confused:
 
  • #7
rl.bhat
Homework Helper
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Okay 20 degrees is 293.15 in Kelvin, and I converted the pressure to pascals. So my equation becomes

[tex](101300)(0.1357)=n(8.314)(293.15)[/tex]

n= 5.64

But why is this still not the right answer? :confused:
Check the volume of the gas.
V = 4/3*π*r^3
 
  • #8
inutard
93
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= [. I said that earlier. I'm sad now.
 

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