Final answer:
In this case, using Boyle's Law, the new volume after the pressure is increased to 2.30 mmHg at constant temperature will be approximately 1.993 m³.
Step-by-step explanation:
According to Boyle's Law, when the pressure of a gas is increased at constant temperature, its volume decreases.
In this case, the initial volume is given as 4.000 m³ and the initial pressure is 1.15 mmHg. If the pressure is increased to 2.30 mmHg while keeping the temperature constant, we can use Boyle's Law to find the new volume.
Boyle's Law states that the product of the initial pressure and initial volume is equal to the product of the final pressure and final volume, when the temperature and amount of gas are kept constant.
So, using Boyle's Law:
(1.15 mmHg) * (4.000 m³) = (2.30 mmHg) * (new volume)
Simplifying the equation, we can find the new volume:
new volume = (1.15 mmHg * 4.000 m³) / 2.30 mmHg
Calculating the above, the new volume is approximately 1.993 m³.