Boyle's Law states that at constant temperature, the pressure and volume of a gas are inversely proportional, and it can be represented by the equation PV = k, where P is the pressure of the gas, V is the volume of the gas, and k is a constant.
In this problem, we are given the initial temperature (25.0°C), the initial volume (10.0 L) and pressure (667 torr), and the final volume (7.88 L). We need to find the final pressure (P2) at constant temperature (25.0°C).
By using the Boyle's law equation, we can calculate the pressure when the volume of the gas is reduced by using the following formula:
P1V1 = P2V2
where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
We can now substitute the given values in the equation:
667 torr * 10.0 L = P2 * 7.88 L
We can then solve for P2:
P2 = (667 torr * 10.0 L) / 7.88 L
P2 = 846.34 torr
So the final pressure when the volume is reduced to 7.88 L at a constant temperature of 25.0°C is 846.34 torr.
It's important to note that this relationship applies only to an ideal gas, and it is only approximation when it is used for real gases.