Kinetic Molecular Theory
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AP Chemistry › Kinetic Molecular Theory
A sample of helium gas is in a cylinder fitted with a frictionless movable piston. The gas is compressed slowly at constant temperature so that the volume is cut in half. Which kinetic molecular theory description best accounts for the change in pressure?
The average kinetic energy increases during isothermal compression, so the pressure increases due to faster particles.
Intermolecular attractions increase during compression and reduce collisions with the walls, causing the pressure to decrease.
The particles gain mass during compression, so collisions become more frequent and the pressure increases.
The particles slow down as the volume decreases, so each collision transfers less momentum and the pressure increases.
The particles collide with the piston more frequently because they have less distance to travel, increasing the pressure.
Explanation
This question tests the understanding of the kinetic-molecular theory, focusing on how volume changes at constant temperature affect collision frequency and gas pressure. In the kinetic-molecular theory, gas pressure arises from particle collisions with the container walls, and at constant temperature, the average kinetic energy and speed remain unchanged. When the helium gas is compressed to half its volume isothermally, the particles have less distance to travel between walls, leading to more frequent collisions and thus doubled pressure, consistent with Boyle's law. The frictionless piston allows slow compression without temperature change, maintaining constant average speed. A tempting distractor is choice E, which wrongly claims average kinetic energy increases during isothermal compression, based on the misconception that compression adds energy rather than just altering spatial distribution. For similar isothermal gas law problems, remember that temperature constancy implies unchanged kinetic energy, and focus on how volume affects collision rates.
A rigid container holds an ideal gas. The pressure increases after the container is heated. Which kinetic molecular theory statement most directly links heating to increased pressure?
Heating decreases the number of particles striking the wall, so the remaining collisions produce higher pressure.
Heating increases the molar mass of the gas, so each collision exerts greater force, increasing pressure.
Heating increases the average kinetic energy, so particles transfer more momentum per wall collision, increasing pressure.
Heating decreases the volume available to the particles, so pressure increases even at constant volume.
Heating increases the attractive forces, so particles pull inward on the walls, increasing pressure.
Explanation
This question tests the understanding of the kinetic molecular theory, specifically linking temperature to pressure via kinetic energy. Kinetic molecular theory explains that heating increases average kinetic energy, causing faster particle motion and greater momentum transfer during wall collisions. In the rigid container, this leads to higher pressure as particles hit walls more forcefully, directly as in choice A. The principle ties temperature to KE = (3/2)kT per particle. Choice C is a tempting distractor, suggesting heating increases molar mass, reflecting the misconception that temperature alters particle properties beyond motion. Always connect gas law observations to microscopic behaviors like kinetic energy and collision dynamics for a deeper understanding.
A student compares diffusion of $\mathrm{NH_3(g)}$ and $\mathrm{HCl(g)}$ at the same temperature in a long tube. Using kinetic molecular theory, which statement best explains why one gas diffuses faster?
$\mathrm{HCl}$ diffuses faster because it has stronger intermolecular attractions that pull it through the tube.
$\mathrm{NH_3}$ diffuses faster because at the same temperature it has a higher average speed due to its lower molar mass.
$\mathrm{HCl}$ diffuses faster because at the same temperature it has a higher average kinetic energy due to its higher molar mass.
Both diffuse at the same rate because gases at the same temperature have the same average speed.
$\mathrm{NH_3}$ diffuses faster because it has a higher temperature than $\mathrm{HCl}$ in the same tube.
Explanation
This question tests the understanding of the kinetic molecular theory, focusing on how molar mass influences diffusion rates at constant temperature. Kinetic molecular theory indicates that at the same temperature, lighter gases have higher average speeds since speed is inversely proportional to the square root of molar mass. In the tube with NH₃ and HCl at the same temperature, NH₃ (lower molar mass) diffuses faster due to its higher speed, as in choice B. This explains why NH₃ travels farther before reacting. Choice C is a tempting distractor, claiming HCl has higher kinetic energy, based on the misconception that heavier gases have more energy, whereas kinetic energy is equal at equal temperatures. For diffusion problems, use Graham's law or the speed-molar mass relationship to predict relative rates.
A sample of an ideal gas is compressed rapidly in a cylinder with a movable piston, decreasing the volume while the temperature is held constant. Using kinetic molecular theory, which statement best explains the change in pressure?
The average kinetic energy decreases because the particles have less space, so the pressure decreases.
The particles move faster during compression at constant temperature, so the pressure increases due to increased speed.
The particles experience stronger attractions at smaller volume, so they collide less often and pressure decreases.
The particles become heavier when compressed, so the pressure increases due to increased particle mass.
The particles collide with the container walls more frequently, increasing the pressure even though their average speed stays the same.
Explanation
This question tests the understanding of the kinetic molecular theory, particularly how volume changes affect gas pressure at constant temperature. In kinetic molecular theory, at constant temperature, the average kinetic energy and speed of particles remain unchanged, but decreasing volume increases the frequency of wall collisions. For the ideal gas compressed in the cylinder with constant temperature, the reduced space means particles hit the walls more often, leading to higher pressure as in choice B. This explanation aligns with the theory that pressure is proportional to collision rate, which rises inversely with volume. Choice E is a tempting distractor, wrongly stating particles move faster during compression, based on the misconception that compression alters kinetic energy independently of temperature. A transferable strategy is to remember that at constant temperature, particle speed is fixed, and pressure changes arise from variations in collision frequency due to volume or particle number.
A balloon filled with air is moved from a warm room to a colder outdoor environment. The balloon remains flexible and the external pressure is approximately constant. Using kinetic molecular theory, which statement best explains why the balloon volume decreases?
Gas particles lose mass in the cold, so fewer collisions occur and the balloon shrinks.
Attractive forces between gas particles increase and pull the balloon inward, decreasing volume without changing particle motion.
Gas particles slow down, so collisions with the balloon wall are less forceful; the balloon contracts until internal and external pressures match.
Gas particles collide more forcefully in the cold, so the balloon volume decreases to reduce collision force.
Gas particles speed up in the cold, so they strike the wall more often and the balloon contracts.
Explanation
This question tests the understanding of the kinetic molecular theory, particularly how temperature decrease affects gas volume at constant pressure. Kinetic molecular theory explains that cooling reduces average kinetic energy, slowing particles and decreasing the force and frequency of wall collisions. For the flexible balloon moved to a colder environment with constant external pressure, the slower particles cause less internal pressure, so the balloon contracts until pressures equilibrate, as in choice A. This volume decrease compensates for reduced collision impacts. Choice D is a tempting distractor, claiming particles speed up in the cold, based on the misconception that cooling increases motion, which contradicts the direct temperature-kinetic energy link. When evaluating volume changes, consider how temperature influences collision dynamics to maintain pressure balance with the surroundings.
A fixed amount of an ideal gas is in a rigid container. The temperature is increased, and the pressure increases. Which statement best describes what happens to the distribution of molecular speeds?
The distribution becomes narrower because all molecules move closer to the same speed at higher temperature.
The distribution shifts to lower speeds because higher temperature increases attractions that slow molecules down.
The distribution shifts to higher speeds only for heavier molecules, because temperature increases molar mass.
The distribution shifts to higher speeds and becomes broader, meaning a greater fraction of molecules have higher speeds.
The distribution does not change because temperature affects only pressure, not molecular motion.
Explanation
This question tests understanding of how temperature affects the Maxwell-Boltzmann distribution of molecular speeds. When temperature increases in a rigid container, the average kinetic energy of gas molecules increases, causing the entire distribution of molecular speeds to shift toward higher values. Additionally, the distribution becomes broader because the range of molecular speeds increases at higher temperatures, with some molecules moving much faster than the average while others move more slowly. This results in a greater fraction of molecules having speeds significantly above the mean. Choice C incorrectly suggests the distribution narrows at higher temperature, when actually the opposite occurs. To visualize temperature effects on molecular motion, remember that higher temperature always shifts the speed distribution to the right and broadens it.
A student adds the same amount of thermal energy to two separate rigid containers, one containing $\text{He}(g)$ and the other containing $\text{Kr}(g)$, each initially at the same temperature. The temperature of each gas increases by the same amount. Which statement is consistent with kinetic molecular theory about the change in molecular speeds?
The average speed of krypton increases more because heavier particles gain more speed for the same temperature increase.
The average speed of helium increases more because at any given temperature helium has a higher average speed than krypton due to its lower molar mass.
Neither gas changes speed because temperature changes pressure but does not affect particle motion directly.
Both gases increase to the same average speed because the temperature increase is the same in both containers.
The average speed increase is the same because intermolecular attractions dominate the motion for both noble gases.
Explanation
This question tests understanding of how molecular mass affects the relationship between temperature change and speed change. When the same amount of thermal energy is added to equal amounts of He and Kr, both gases experience the same temperature increase. However, since helium has a much lower molar mass than krypton, helium molecules must increase their speed more to achieve the same increase in average kinetic energy. This follows from KE = ½mv²: for the same ΔKE, a lighter particle must have a larger Δv. Additionally, helium already has a higher initial speed than krypton at the same starting temperature, so its speed increase is proportionally larger. Choice B incorrectly suggests heavier particles gain more speed, reversing the actual relationship. To compare speed changes for different gases, remember that lighter gases always experience larger speed changes for the same temperature change.
A sample of $\text{CO}_2(g)$ in a flexible balloon is taken from a warm room to a cold outdoor environment. The balloon’s volume decreases. Which kinetic molecular theory statement best connects the temperature change to the observed volume change (assuming external pressure is constant)?
Lower temperature strengthens attractions enough to increase the gas pressure, forcing the balloon to contract.
Lower temperature means lower average molecular kinetic energy, so the gas exerts less pressure unless the volume decreases to maintain balance with the external pressure.
Lower temperature increases the molar mass of $\text{CO}_2$, so the balloon shrinks because heavier gases occupy less space.
Lower temperature increases the number of $\text{CO}_2$ molecules, so the balloon shrinks to keep pressure constant.
Lower temperature increases the size of $\text{CO}_2$ molecules, so the balloon must shrink to fit the larger particles.
Explanation
This question tests understanding of how temperature changes affect gas volume at constant external pressure. When the CO₂ gas is cooled from the warm room to the cold outdoors, the average kinetic energy of the molecules decreases, causing them to move more slowly. With slower molecular motion, the gas molecules exert less pressure on the balloon walls due to both reduced collision frequency and less momentum transfer per collision. Since the external atmospheric pressure remains constant, the balloon must shrink until the internal pressure increases enough (through higher collision frequency in the smaller volume) to balance the external pressure. Choice E incorrectly suggests that attractions increase pressure, when actually intermolecular attractions would slightly decrease pressure if they had any effect. To predict volume changes, remember that at constant pressure, gas volume is directly proportional to absolute temperature (Charles's Law).
A student compares two samples of the same gas in identical rigid containers. Sample 1 is at a higher temperature than Sample 2. Which statement best describes the effect of temperature on molecular collisions with the container walls?
In Sample 1, the number of molecules increases as temperature rises, so collisions become more frequent.
In Sample 1, molecules collide less often because faster molecules spend less time near the walls.
In Sample 1, molecules become heavier, so they collide with less force even though temperature is higher.
In Sample 1, molecules have greater average kinetic energy, so collisions with the walls transfer more momentum per collision on average.
In Sample 1, increased attractive forces reduce collision force, so pressure should decrease in a rigid container.
Explanation
This question tests understanding of how temperature affects molecular collisions with container walls. In Sample 1 at higher temperature, gas molecules have greater average kinetic energy, which means they move faster on average. These faster-moving molecules collide with the container walls more frequently and, more importantly, transfer more momentum per collision due to their higher speeds. The combination of increased collision frequency and greater momentum transfer per collision results in higher pressure in Sample 1. Choice B incorrectly suggests that faster molecules collide less often, when actually both collision frequency and force increase with temperature. To analyze pressure differences, remember that pressure depends on both how often molecules hit the walls and how hard they hit, both of which increase with temperature.
A rigid container holds a mixture of two ideal gases, $\text{H}_2(g)$ and $\text{O}_2(g)$, at the same temperature. Which statement is consistent with kinetic molecular theory?
The $\text{H}_2$ molecules have lower average kinetic energy because they have smaller molar mass.
The $\text{O}_2$ molecules have higher average speed because heavier molecules move faster at the same temperature.
Both gases have the same average speed because they are in the same container and collide with each other.
Both gases have the same average kinetic energy, but $\text{H}_2$ molecules have a higher average speed than $\text{O}_2$ molecules.
The $\text{O}_2$ molecules have higher average kinetic energy because they have stronger intermolecular attractions.
Explanation
This question tests understanding of kinetic molecular theory for gas mixtures at thermal equilibrium. When different gases are mixed in the same container at the same temperature, they all have the same average kinetic energy regardless of their molecular masses. Since KE = ½mv², and H₂ has a much lower molar mass (2 g/mol) than O₂ (32 g/mol), hydrogen molecules must have a higher average speed to achieve the same kinetic energy. Specifically, the speed ratio is vH₂/vO₂ = √(mO₂/mH₂) = √16 = 4, meaning H₂ molecules move on average 4 times faster than O₂ molecules. Choice B incorrectly claims both gases have the same speed, ignoring the inverse relationship between mass and speed at constant kinetic energy. To analyze gas mixtures, remember that temperature determines average kinetic energy, which is the same for all gases, but molecular speeds vary inversely with the square root of molar mass.