Final answer:
When solving for the volume of a gas (V2) using Boyle's Law and the initial pressure (P1) is greater than the final pressure (P2), the resulting V2 is expected to be larger than the initial volume (V1) because pressure and volume are inversely proportional.
Step-by-step explanation:
If P1 is greater than P2, and we are using the formula P₁V₁ = P₂V₂ to solve for the volume of a gas (V2), we would expect the resulting V2 to be larger than V1. This is because the formula illustrates Boyle's Law, which states that for a constant temperature and amount of gas, the pressure and volume of a gas are inversely proportional. If the initial volume is V1 and the pressure decreases from P1 to P2, the gas must expand to increase its volume to V2 in order to maintain the equality of the formula.
For example, using P₁ and V₁ as the known values (13.0 psi and 15.0 mL), and P2 as the pressure at which the volume is unknown, and V₂ as the unknown volume, the calculation would show an increase in V2 as P2 is lower than P1. The gases move from higher pressure to lower pressure, meaning they expand into a larger volume when the pressure is reduced.
This understanding is further supported by the concept that when a gas occupies a smaller volume, it exerts a higher pressure; conversely, when it occupies a larger volume, it exerts a lower pressure, as stated in the figure description.