Answer:
The volume of the balloon would be 374 L.
Explanation:
Initially, He occuplies a volume of 17.0 L (V₁) at a pressure of 22.0 atm (P₁). If pressure decreases to 1.00 atm (P₂), volume is expected to increase. Assuming ideal behavior of the gas and constant temperature, we can calculate the final volume (V₂) using Boyle's Law.
[tex]P_{1} \times V_{1} = P_{2} \times V_{2}\\V_{2} = \frac{P_{1} \times V_{1}}{P_{2}} =\frac{22.0atm \times 17.0L}{1.00atm} = 374 L[/tex]
Taking into account the Boyle's law, the volume of the balloon would be 374 L.
An ideal gas is a theoretical gas that is considered to be composed of point particles that move randomly and do not interact with each other. Gases in general are ideal when they are at high temperatures and low pressures.
The gas laws are a set of chemical and physical laws that allow determining the behavior of gases in a closed system. The parameters evaluated in these laws are pressure, volume, temperature and moles.
Pressure and volume are related by Boyle's law (one of the gas laws), which says that the volume occupied by a given mass of gas at constant temperature is inversely proportional to pressure.
Boyle's law is expressed mathematically as:
P×V = k
Studying an initial state 1 and a final state 2, it is satisfied:
P1×V1 = P2×V2
In this case, you know:
Replacing:
22 atm× 17 L= 1 atm× V2
Solving
[tex]V2=\frac{22atmx17 L}{1 atm}[/tex]
V2= 374 L
Finally, the volume of the balloon would be 374 L.
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