### Video Transcript

Which of the following will cause the pressure of a gas to decrease? (I) Increasing the volume, with the temperature held constant. (II) Decreasing the volume and increasing the temperature. (III) Increasing the temperature, with the volume held constant. (A) I only, (B) II only, (C) I and II only, (D) II and III only, or (E) I, II, and III.

In this question, we need to determine how changing different properties of a gas will cause the pressure to change. Pressure is defined as a force that’s exerted over a certain area. This means that the pressure of a gas is caused by the collisions of the gas particles with the walls of the container. So let’s think about how statement (I), increasing the volume with the temperature held constant, will affect the pressure of a gas.

If we increase the volume of the gas, the gas particles will have more room in their container. So they will go longer between collisions with the walls of the container. Because there will be fewer collisions between the gas particles and the container, the pressure will be lower. So increasing the volume while holding the temperature constant will cause the pressure of a gas to decrease. To think about this statement, we can also use Boyle’s law, which is a gas law that tells us that the pressure times the volume are equal to a constant at constant temperature.

Boyle’s law tells us that the pressure and volume are inversely proportional. So when the volume goes up, the pressure goes down, and vice versa. Either way, increasing the volume of the gas will cause the pressure of the gas to decrease. Now, let’s move on to statement (III) because it also only has one variable we’re changing, increasing the temperature with the volume held constant.

Temperature and kinetic energy are directly proportional. So when we increase the temperature of a gas, it will cause the kinetic energy to increase as well. The kinetic energy is also related to the speed that the gas particles are moving. So if the kinetic energy is higher, the particles of gas will be moving faster.

So a higher temperature means that the particles of gas will be moving faster, which means that they will collide more frequently with the walls of their container. And since there’ll be more collisions with the walls of the container, that means the pressure will be higher. So increasing the temperature while holding the volume constant will cause the pressure to increase, not decrease. To think about this statement, we could also use Gay-Lussac’s law, which tells us that the pressure divided by the temperature is equal to a constant at constant volume.

So Gay-Lussac’s law tells us that the pressure and temperature are directly proportional, which means that when the temperature increases, so does the pressure, and vice versa. Either way, increasing the temperature with the volume held constant will cause the pressure of the gas to increase, not decrease.

In statement (II), we have two variables that we need to think about. We’ll be decreasing the volume and increasing the temperature. So we’ve thought about the volume and the temperature and its effect on the pressure of a gas individually. So let’s think about how these two changes will cause the pressure of the gas to change. We’ve just discussed how increasing the temperature causes the pressure of the gas to increase because the particles will be moving faster. So they will collide with the walls of their container more frequently, meaning that the pressure will be higher.

We’ve also discussed how increasing the volume of the gas causes there to be more room for the gas particles to move around, meaning they’ll have fewer collisions with the walls of their container. So the pressure will decrease. This statement says that we’re decreasing the volume, so the opposite will be true. When we decrease the volume, there will be less room for the gas particles. Meaning that they’ll collide with the walls of their container more frequently, which will cause the pressure to increase. So both of these changes cause an increase in the pressure.

So statement (II) decreasing the volume and increasing the temperature would not decrease the pressure of a gas. To think about this statement, we can also use the combined gas law, which tells us that the pressure times the volume divided by the temperature is equal to a constant. So we could use this gas law to create an expression that we can play with to determine how the pressure of the gas would change if we decrease the volume and increase the temperature. To make the numbers easier, we could imagine having the volume and doubling the temperature.

If we rearrange the previous expression, we’ll end up with something that we can use to solve for 𝑃 two. And then, if we plug our final temperatures and volumes in, we can solve for 𝑃 two. We would find that if we were to decrease the volume by halving it and increase the temperature by doubling it, the pressure would be four times the original pressure. Either way, we’ll find that decreasing the volume and increasing the temperature would increase the pressure, not decrease it.

Since only statement (I) caused the pressure of a gas to decrease, this matches answer choice (A).