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How many moles of gas are in the balloon?

  • Thread starter roam
  • Start date
1,265
11
1. 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?

3. 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.
 

rl.bhat

Homework Helper
4,433
5
Given pressure is in kilopascal.
Temperature must be in Kelvin.
 
Last edited:

mgb_phys

Science Advisor
Homework Helper
7,744
11
Temperature should be in kelvin
 

rock.freak667

Homework Helper
6,230
31
Your temperature should be in Kelvin (K) and the pressure in Pa
 
93
0
Also, you squared your radii instead of cubing it.
 
1,265
11
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:
 

rl.bhat

Homework Helper
4,433
5
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
 
93
0
= [. I said that earlier. I'm sad now.
 

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