In: Chemistry
When the balloon is filled with He at sea level we can find the amount of He in it using the formula. Here pressure is 760 mmHg which is 1 atm, assuming 25 oC which is 298 K
PV=nRT
1 atm x 6.5 L = n x 0.082057 L atm K−1 mol−1 x 298 K
n = (1 atm x 6.5 L)/0.082057 L atm K−1 mol−1 x 298 K
n = 0.266 moles of He
Now when it rises from sea level to a height where the pressure is 700 mm Hg that is 0.921 atm the number of moles remains the same.
PV= nRT
0.921 atm x V = 0.266mol x 0.082057 L atm K−1 mol−1 x 298 K
V = (0.266 mol x 0.082057 L atm K−1 mol−1 x 298 K)/0.921 atm
V = 7.057 L
So the volume of gas in the ballon will be greater than that at sea level
This is well explained by Boyle's law which states
The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.
Mathematically, Boyle's law can be stated as
So when pressure decreases volume increases