Calculation of the Volume of a Gas-filled Balloon

Given:

• Gas pressure (P): 8.31 x 10^5 Pa
• Gas temperature (T): 300 K
• Amount of substance (n): 100 mol

To find:

• Volume of the balloon

Solution:

1. Convert the gas pressure from Pascals to atmospheres (1 atm = 101325 Pa):
   • P = 8.31 x 10^5 Pa / 101325 Pa/atm
   • P = 8.18 atm
2. Apply the ideal gas law equation: PV = nRT
   • P: pressure (in atm)
   • V: volume (in liters)
   • n: amount of substance (in moles)
   • R: ideal gas constant (0.0821 L·atm/(mol·K))
   • T: temperature (in Kelvin)
3. Rearrange the equation to solve for V:
   • V = (nRT) / P
4. Substitute the given values into the equation:
   • V = (100 mol 0.0821 L·atm/(mol·K) 300 K) / 8.18 atm
5. Calculate the volume of the balloon:
   • V = 301.47 L

Therefore, the volume of the gas-filled balloon is approximately 301.47 liters.