How many moles of gas are in the balloon?

[roam]

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 $$PV=nRT$$

Volume is $$v=\frac{4}{3} \pi (0.18)^2 = 0.1357$$

R is the constant 8.314

So $$(101.3)(0.1357)=n8.314(20)$$

Now if I solve for n I get $$n= {13.74}{166.28} = 0.082$$

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]

Given pressure is in kilopascal.
Temperature must be in Kelvin.

 

[mgb_phys]

Temperature should be in kelvin

 

[rock.freak667]

Your temperature should be in Kelvin (K) and the pressure in Pa

 

[inutard]

Also, you squared your radii instead of cubing it.

 

[roam]

Okay 20 degrees is 293.15 in Kelvin, and I converted the pressure to pascals. So my equation becomes

$$(101300)(0.1357)=n(8.314)(293.15)$$

n= 5.64

But why is this still not the right answer?

 

[rl.bhat]

Okay 20 degrees is 293.15 in Kelvin, and I converted the pressure to pascals. So my equation becomes

$$(101300)(0.1357)=n(8.314)(293.15)$$

n= 5.64

But why is this still not the right answer?

Check the volume of the gas.
V = 4/3*π*r^3

 

[inutard]

= [. I said that earlier. I'm sad now.