A sample of nitrogen gas at 298 K and 745 torr has a volume of 37.42 L. What volume will it occupy if the pressure is increased to 894 torr at constant temperature?

This problem can be solved using the ideal gas law, which states that the pressure of a gas times its volume is proportional to the number of gas molecules and the temperature of the gas. However, since the number of molecules and the temperature are constant in this problem, we can simplify the ideal gas law to Boyle's law, which states that the pressure of a gas is inversely proportional to its volume at a constant temperature.

Boyle's law can be written as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

1. First, convert the pressures from torr to atm, since the ideal gas law uses atm. 1 atm = 760 torr, so P1 = 745 torr * (1 atm / 760 torr) = 0.980263 atm and P2 = 894 torr * (1 atm / 760 torr) = 1.17632 atm.

2. Substitute the known values into Boyle's law: (0.980263 atm * 37.42 L) = (1.17632 atm * V2).

3. Solve for V2: V2 = (0.980263 atm * 37.42 L) / 1.17632 atm = 31.07 L.

So, if the pressure is increased to 894 torr at constant temperature, the volume of the nitrogen gas will decrease to 31.07 L.