The weight of the balloon is irrelevant because it is the gas that lifts it in the air. We are already given with the required volume, so we use this instead. The atomic weight of zinc is 65.38 g/mol. Assuming ideal gas behavior,
PV=nRT
P(475 mL)(1 L/1000 mL) = (1.85/65.38)(0.0821 L·atm/mol·K)(21.5 + 273)
P = 1.44 atm
Then, we use this pressure and the volume to find the moles of zinc.
(1.44 atm)(475 mL+1 mL)(1 L/1000 mL) = n(0.0821 L·atm/mol·K)(21.5 + 273)
Solving for n,
n = 0.02836 moles of zinc