### Instruction: At constant temperature, the pressure of a sample of gas is inversely proportional to its volume. I have some hydrogen in a 3.67 liter container with a pressure of 4 kPa. If I move all of it to a 1.835 liter container at the same temperature, what will the new pressure be in kPa?### Response: I recognize this as an example of Boyle's law, which states that PV = k for a fixed amount of gas at constant temperature, where P is pressure, V is volume, and k is a constant.
I can use this equation to relate the initial and final states of the gas.
Let P1 and V1 be the initial pressure and volume, and P2 and V2 be the final pressure and volume.
Then I have:

P1V1 = k = P2V2
I can solve for P2 by dividing both sides by V2:

P2 = (P1V1)/V2
Now I can plug in the given values for P1, V1, and V2.
I have:

P2 = (4 kPa)(3.67 L)/(1.835 L)