# Buoyant force on a balloon is equal to the mass of air it displaces

#### chemguy12345

1. The problem statement, all variables and given/known data

The buoyant force on a balloon is equal to the mass of air it displaces. The gravitational force on the balloon is equal to the sum of the masses of the balloon, the gas it contains, and the balloonist. If the balloon and balloonist together weight 175 kg, what would the diameter of a spherical hydrogen-filled balloon have to be in meters if the rig is to get off the ground at 22 degrees Celsius and 752 mmHg? (Take MM air= 29.0 g/mol)

2. Relevant equations

We're currently studying gases. So I'm thinking of finding mass of h2 gas and then the moles of H2, then the volume and plugging into V=(4/3)(Pi)(r^3) to find radius and then diameter. Relevant Equations --> V=nRT/P. (r=.0821 atm L/mol K), PV=nRT(ideal gas law)

3. The attempt at a solution
I don't know where to begin. The wording is confusing me. Help please
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### Borek

Mentor
Re: Gases-chemistry

You need to calculate first what volume will have buoyancy high enough.

#### chemguy12345

Re: Gases-chemistry

What formula would I have to use? I'm not sure because we haven't learned anything about buoyancy yet. Thank you for helping

#### Borek

Mentor
Re: Gases-chemistry

Buoyancy is physics, but you are told how to calculate it - it equals mass (I would say weight) of the air balloon displaces.

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