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

[chemguy12345]

Homework Statement

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)

Homework 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)

The Attempt at a Solution

I don't know where to begin. The wording is confusing me. Help please

 

[Borek]

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

 

[chemguy12345]

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]

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

 

[DeeNos]

I would first start by identifying the given information and any relevant equations to use. It appears that we are dealing with the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas. We are also given the gravitational force on the balloon, which is equal to the sum of the masses of the balloon, the gas it contains, and the balloonist. We can use this information to find the mass of the hydrogen gas in the balloon.

Next, we need to determine the volume of the balloon. Since we are given the diameter of the balloon, we can use the formula for the volume of a sphere (V = (4/3)πr^3) to find the volume. From there, we can use the ideal gas law (PV = nRT) to solve for the number of moles of hydrogen gas in the balloon.

Once we have the number of moles, we can use the molar mass of hydrogen (MM H2 = 2 g/mol) to find the mass of the hydrogen gas in the balloon. From there, we can subtract the mass of the balloon and the balloonist (175 kg) to find the mass of air that the balloon displaces.

Finally, we can use the given information that the buoyant force is equal to the mass of air displaced to solve for the volume of air displaced. This will give us the volume of air that the balloon needs to displace in order to lift off the ground. We can then use this information to find the required diameter of the balloon using the formula for the volume of a sphere.