Final answer:
Using Boyle's law, which expresses the inverse relationship between pressure and volume of a gas, the new volume when the pressure is increased by a factor of 5 is found to be 1.5 liters.
Step-by-step explanation:
To determine the new volume of a gas when the pressure is increased by a factor of 5, we can use Boyle's law, which states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. Boyle's law can be expressed as P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume respectively.
Given that the initial volume (V₁) is 7.5 L and the pressure is increased by a factor of 5, we can express this as P₂ = 5P₁. Substituting the known values into Boyle's law gives us:
7.5 L × P₁ = V₂ × 5P₁
Since P1 is on both sides of the equation, it cancels out and we can solve for V₂:
V₂ = 7.5 L / 5
V₂ = 1.5 L
Therefore, the new volume of the gas when the pressure is increased by a factor of 5 is 1.5 liters.