Final answer:
Using Boyle's Law, the final volume of a balloon originally at 650 kPa and 2.2 L, when expanded to a final pressure of 115 kPa, would be approximately 12.43 L. This calculation assumes the temperature remains constant and applies the relationship between pressure and volume.
Step-by-step explanation:
Understanding Gas Laws for Balloon Expansion
The original question presents a scenario where a balloon filled with hydrogen gas experiences a change in pressure, resulting in a change in volume. We use the Combined Gas Law to solve for the final volume of the balloon. This law combines Charles's Law, Boyle's Law, and Gay-Lussac's Law into a single equation that relates pressure (P), volume (V), and temperature (T) of a gas: P₁V₁/T₁ = P₂V₂/T₂. Assuming temperature remains constant, the equation simplifies to Boyle's Law: P₁V₁ = P₂V₂. To find the final volume of the balloon (V₂), we rearrange the equation to V₂ = P₁V₁ / P₂.
Given:
- Initial Pressure (P₁): 650 kPa
- Initial Volume (V₁): 2.2 L
- Final Pressure (P₂): 115 kPa
We can calculate the final volume (V₂) using the given values:
V₂ = (650 kPa * 2.2 L) / 115 kPa
After performing the calculation, we can find that the final volume of the balloon is approximately 12.43 L. This example demonstrates how gas laws can be applied to predict how the volume of a gas changes with pressure when temperature is held constant.