To solve this problem, we can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The equation for Boyle's law is as follows:
P₁ * V₁ = P₂ * V₂
Where: P₁ = Initial pressure V₁ = Initial volume P₂ = Final pressure V₂ = Final volume
Given: Initial volume (V₁) = 750 ml Initial pressure (P₁) = 700 torr Final pressure (P₂) = 100 torr
We need to find the final volume (V₂).
Using the given values, we can rearrange the Boyle's law equation to solve for V₂:
V₂ = (P₁ * V₁) / P₂
Substituting the given values into the equation:
V₂ = (700 * 750) / 100
V₂ = 5250 / 100
V₂ = 52.5 ml
Therefore, the new volume of the gas, when the pressure has increased from 700 torr to 100 torr, will be 52.5 ml.