There are 600 molecules of gas in an airtight container, and the volume is held constant. Which changes would cause the greatest DECREASE in pressure? a releasing 200 molecules and increasing the temperature by 20 K b adding 200 more molecules and decreasing the temperature by 20 K c releasing 200 molecules and decreasing the temperature by 20 K d adding 200 more molecules and increasing the temperature by 20
The greatest decrease in pressure will occur with option c) releasing 200 molecules and decreasing the temperature by 20 K.
Decreasing the number of molecules reduces the number of collisions happening in the container, resulting in a decrease in pressure. Additionally, decreasing the temperature decreases the average kinetic energy of the molecules, which further reduces their speed and the number of collisions, leading to a decrease in pressure.
To determine which changes would cause the greatest decrease in pressure, we need to analyze the effects of each change on the pressure of the gas in the container.
(a) Releasing 200 molecules and increasing the temperature by 20 K:
Releasing 200 molecules means the total number of molecules will decrease from 600 to 400. As a result, the pressure will decrease since there are fewer molecules colliding with the walls of the container. Increasing the temperature will cause the molecules to move faster, leading to more frequent and energetic collisions, which will increase the pressure. Therefore, this change will not result in a significant decrease in pressure.
(b) Adding 200 more molecules and decreasing the temperature by 20 K:
Adding 200 molecules means the total number of molecules will increase from 600 to 800. As a result, the pressure will increase since there are more molecules colliding with the walls of the container. Decreasing the temperature will cause the molecules to move slower, resulting in less frequent and energetic collisions, which will decrease the pressure. Therefore, this change will not cause a significant decrease in pressure.
(c) Releasing 200 molecules and decreasing the temperature by 20 K:
As mentioned earlier, releasing 200 molecules will decrease the total number of molecules from 600 to 400, leading to a decrease in pressure. Additionally, decreasing the temperature will cause the molecules to move slower, resulting in less frequent and energetic collisions, which will further decrease the pressure. Therefore, this change will cause a notable decrease in pressure.
(d) Adding 200 more molecules and increasing the temperature by 20 K:
Adding 200 molecules will increase the total number of molecules from 600 to 800, leading to an increase in pressure. Additionally, increasing the temperature will cause the molecules to move faster, resulting in more frequent and energetic collisions, which will further increase the pressure. Therefore, this change will not cause a decrease in pressure.
In conclusion, the change that would cause the greatest decrease in pressure is option (c) releasing 200 molecules and decreasing the temperature by 20 K.
To determine which changes would cause the greatest decrease in pressure, let's analyze each option:
a) Releasing 200 molecules and increasing the temperature by 20 K:
When molecules are released, the number of gas molecules decreases. In this case, 200 molecules are released, leaving a total of 600 - 200 = 400 molecules. Since the volume is constant, the pressure is inversely proportional to the number of gas molecules (according to the ideal gas law).
Moreover, when the temperature increases, the kinetic energy of gas molecules also increases. Higher kinetic energy leads to an increase in the pressure (directly proportional to temperature).
So, in this case, the decrease in pressure due to releasing 200 molecules is counteracted by the increase in pressure caused by the increase in temperature. Therefore, the overall change will likely result in a lesser decrease in pressure.
b) Adding 200 more molecules and decreasing the temperature by 20 K:
When more molecules are added to the container, the number of gas molecules increases. In this case, the total number of molecules becomes 600 + 200 = 800. Again, keeping the volume constant, the pressure is inversely proportional to the number of gas molecules.
Additionally, when the temperature decreases, the kinetic energy of gas molecules decreases. Lower kinetic energy leads to a decrease in pressure. Hence, decreasing the temperature causes a decrease in pressure.
In this case, both the addition of 200 molecules and the decrease in temperature contribute to a decrease in pressure. The decrease in pressure due to decreasing the temperature would likely outweigh the increase in pressure caused by the addition of more molecules. Therefore, this option would result in the greatest decrease in pressure.
c) Releasing 200 molecules and decreasing the temperature by 20 K:
This scenario is similar to option b as it involves the release of 200 molecules, leaving 600 - 200 = 400 molecules. Additionally, there is a decrease in temperature, which would also lead to a decrease in pressure.
Similar to option b, both the decrease in the number of gas molecules and the decrease in temperature contribute to a decrease in pressure. Therefore, this option could result in a significant decrease in pressure, but it may not be as significant as adding 200 more molecules (option b).
d) Adding 200 more molecules and increasing the temperature by 20 K:
When molecules are added, the number of molecules increases. In this case, the total number becomes 600 + 200 = 800. As mentioned before, the pressure is inversely proportional to the number of gas molecules when the volume is held constant.
Additionally, increasing the temperature causes an increase in kinetic energy, resulting in an increase in pressure. So, both the addition of molecules and the increase in temperature would lead to an increase in pressure, making this option the least likely to cause a decrease.
Considering all the explanations, option b (adding 200 more molecules and decreasing the temperature by 20 K) would likely cause the greatest decrease in pressure among the given choices.