A weather balloon is designed to expand to
a maximum radius of 30 m when in flight at
its working altitude where the air pressure is
0.033 atm and the temperature is 95 K.
If the balloon is filled at atmospheric pres-
sure and 462 K, what is its radius at lift-off?
PV = nRT
Volume = 4/3πr^3
The Attempt at a Solution
First, I used the ideal gas law to find n:
(0.033)(4/3π(30)^3) = n(8.31)(95)
n = 4.727610453 mol
Then, I solved for r:
V = nRT/P
4/3πr^3 = (4.727610453)(8.31)(462)/1 atm
r = 11.30381236 m (WRONG ANSWER)
What am I doing wrong?