To an order of magnitude, how many helium-filled toy balloons would be required to lift you? Because helium is an irreplaceable resource, develop a theoretical answer rather than an experimental answer. Assume that you have a mass of approximately 70 kg, the radius of a balloon is 12.5 cm, the helium is at STP and it is immersed in air at 0°C and 1 atm.

I used the equation for buoyant force to find the buoyant force of one balloon. The equation is Buoyant force= (density of air)*(acceleration due to gravity)*(Volume displaced)

The weight of the person is 686/buoyant force of one one balloon= # of balloons.

I got 6710 balloons, but this is incorrect.

But you left out the weight of the Helium

At stp a mole of Helium is 22.4 liters
and a mole of He is 4 grams / mol

I included the weight of helium, (which is minuscule) and it still did not work.

Just as an update, I did include the weight of the helium, but I did it incorrectly. Thanks for making me check it again. Really, I am truly grateful. THANKS DAMON.

You are welcome :)

To calculate the number of helium-filled toy balloons required to lift you, we need to consider the buoyant force acting on each balloon and the weight of the person. Let's break down the steps to calculate this:

1. Find the volume of one balloon:
The volume of a balloon can be approximated as a sphere. Given the radius of the balloon (12.5 cm), the volume can be calculated using the formula for the volume of a sphere: V = (4/3)πr³.

V = (4/3) * π * (0.125 m)³ [converting radius to meters]
V ≈ 0.00824 m³

2. Determine the buoyant force acting on one balloon:
The buoyant force on an object submerged in a fluid (in this case, air) depends on the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity. The density of air at STP (standard temperature and pressure) is approximately 1.225 kg/m³, and the acceleration due to gravity is about 9.8 m/s².

Buoyant Force = (Density of air) * (Acceleration due to gravity) * (Volume displaced)
Buoyant Force = (1.225 kg/m³) * (9.8 m/s²) * (0.00824 m³)
Buoyant Force ≈ 0.098 N

3. Calculate the number of balloons required to lift a person:
The weight of the person can be approximated as 686 N (mass of 70 kg multiplied by the acceleration due to gravity).

Number of balloons = Weight of person / Buoyant force of one balloon
Number of balloons = 686 N / 0.098 N
Number of balloons ≈ 7,000

So, based on these calculations, approximately 7,000 helium-filled toy balloons would be required to lift a person with a mass of 70 kg under the given conditions.