A helium party balloon, assumed to be a perfect sphere, has a radius of `18.0\ cm`. At room temperature (`20°C`), its internal pressure is `1.05` atm. Find the number of moles of helium in the balloon and the mass of helium needed to inflate the balloon to these values. Given: `r = 18.0\ cm = 0.180\ m` `T = 20°C = 293 K` `P = 1.05\ atm = (1.05 times 1.013) times 10^5 N/m^2 = 1.064 times 10^5 N/m^2` Known: `R =8.314\ J//(mol•K)` Equation: `PV = nRT` Solution: `n = (PV)/(RT)` `n = ((1.064 times 10^5 N//m^2)(4/3π(0.180\ m)^3))/((8.314\ J//(mol•K))(293 K))` The atomic mass of helium is `4.00\ u or 4.00\ g//mol` `m = n times` molecular mass `m = 1.066\ mol times 4.00\ g//mol`