Ideal gas questions and gas 'buoyancy'?

Question

I’ve been out of school for years and have recently been working on a problem that requires the knowledge that seemed irrelevant to me when taking chemistry 101.

(Oddly, every single class I was required to take that taught information I THOUGHT I’d never use, I later found to be crucial, highly useful information.)

Anyways, I believe I’ve figured this out, but just wanted to post these questions to double check my results.

Ideal Gas Law:  PV=kNT, Where 
P=Pressure
V=Volume
k=Boltzmann Constant
N=number of molecules and
T=temperature.

Question 1)  assuming no change in P, k or N:  
if the temperature of a gas is increased from 0 C to 27.315 C, what is the corresponding increase in volume?

Question 2) assuming no change in k or N in a sealed container of Freon under pressure: 
How much pressure is required to increase the temperature of the gas from 0 C to 27.315 C?  (remember that the gas WILL compress under pressure, so the pressure increase has to exceed the volume decrease for any temperature increase to take place)

Question 3) (displacement, lift and buoyancy)     
Dry air has a molecular weight of 28.9644 grams per mol
At a molar volume of 22.4 litres, 0 C and 100 kPascals.
G=9.81 m/(s^2)

What is the maximum density (mass/volume) at which an object can have neutral buoyancy in dry air?

[I understand that the term 'buoyancy' is usually utilized in regards to a solid in a liquid medium, but it seemed an appropriate analogy here.]

Anonymous · Accepted Answer

1) Convert your question to Kelvin for the solution.  
273.15 K increased by 27.315 represents a 10% increase in temperature, so also represents a 10% increase in volume.

2) The answer depends on which Freon you mean.  The term Freon is a name used by Dupont (trademarked) to describe an entire category of chemicals~Chlorofluorocarbons.  (CFCs)
each has distinctive properties.  See the following link for an idea of the pressure to temperature relations due to the compressibility of gasses:
http://en.wikipedia.org/wiki/Compressibility_factor

3) Convert grams and liters to kilos and meters cubed, then use simple division to yield:
1.293045 kilos per meter cubed.  Because the lowest number of decimals in the calculation is one, your solution should represent this, so round up to 1.3 kilos per meter cubed.  Objects below this density will 'float' in normal air at standard pressure~Like SEAgel, one of the newer aerogels.

Hyliston (Eric) · Answer

1&2) As long as you converted your degrees Celsius to Kelvin (or Rankine, I suppose) in each example, the math is pretty straight-forward.  [K] = [Â°C] + 273.15

3) 28.9644g/22.4L at STP.  I have no idea what you need the acceleration due to gravity for (G).

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Ideal gas questions and gas 'buoyancy'?

2 Answers