To solve this problem, we can use Boyle's Law, which states that for a fixed amount of gas at a constant temperature, the pressure and volume are inversely proportional. Mathematically, it can be expressed as:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume, respectively, and P₂ and V₂ are the final pressure and volume.
Given: Initial pressure, P₁ = 738 mmHg Initial volume, V₁ = 4.00 m^3 Final pressure, P₂ = 635 mmHg
Let's calculate the final volume, V₂:
P₁V₁ = P₂V₂
(738 mmHg) (4.00 m^3) = (635 mmHg) V₂
Now we can solve for V₂:
V₂ = (738 mmHg) (4.00 m^3) / (635 mmHg)
V₂ ≈ 4.64 m^3
Therefore, the volume of the gas at a pressure of 635 mmHg, with the temperature remaining unchanged, would be approximately 4.64 m^3.