Determine balloon diameter needed to lift a 7 pound weight with various gases My question is regarding setting up this equation. The givens are as follows:


Gases are helium, methane and hydrogen. (Test all three)
Assume balloon is spherical.
Assume temperature is $25~\mathrm{^\circ C}$


So I need to find the diameter of the balloon needed to lift a 7lb weight. I setup my equation as follows. $$m=\frac{PVM}{RT}$$

Next, I subtract my first gas ($\ce{He}$) from ambient air and convert my $m$ to equal grams in the weight. so I set it up like so.

$$3730.15~\mathrm{g}=\frac{PVM}{RT}-\frac{PVM}{RT}$$

Next I factor out the pressure and volume and fill in my numbers.
$$3730.15~\mathrm{g}=PV\left(\frac{(28.9~\mathrm{g~mol^{-1}})}{(0.0821~\mathrm{L~atm^{-1}mol^{-1}K^{-1}})(298~\mathrm{K})}-\frac{8~\mathrm{g~mol^{-1}}}{(0.0821~\mathrm{L~atm^{-1}mol^{-1}K^{-1}})(298~\mathrm{K})}\right)$$

This is where I am stuck at as I don't know what makes sense to use for pressure so I can solve for volume? Or maybe this is all setup wrong and makes no sense?
For a real balloon, the balloon itself will have mass, and the balloon may have higher pressure inside than atmospheric pressure.  

Absent additional information, for a homework problem, you would assume mass of the balloon is zero and pressure is atmospheric pressure.

Note: in the OP 8g/mol is wrong.