Deviation from Ideal Gas Law - AP Chemistry

A sample of Ar(g) is placed in a rigid container at extremely high pressure. The student expects $Z=\frac{PV}{nRT}$ to equal 1, but finds $Z>1$ . Which statement best explains why $Z$ is greater than 1 under these conditions?
Answer: At very high pressure, excluded volume and repulsive interactions become significant, making the measured $PV$ larger than the ideal value. This question tests understanding of the compressibility factor Z and positive deviations at extreme pressure. At extremely high pressure, argon atoms are forced so close together that two effects dominate: the finite volume of atoms becomes significant relative to container volume, and short-range repulsive forces arise when electron clouds overlap. Both effects increase the measured PV product above the ideal value nRT, making Z > 1. Choice B incorrectly suggests attractive forces would make Z > 1, but attractions actually make Z < 1 by reducing pressure. The key insight is that at extreme pressures, repulsive interactions and excluded volume effects dominate over any attractive forces, causing positive deviations from ideality.
A rigid container holds a gas sample at conditions close to condensation (low temperature and relatively high pressure). A student finds that the measured pressure is lower than the value predicted by $PV=nRT$ for the same $n$ , $V$ , and $T$ . Which statement best explains this result?
Answer: The measured pressure is lower because intermolecular attractions reduce the momentum transferred to the container walls, lowering pressure relative to ideal. This question tests understanding of pressure deviations near condensation conditions. When a gas is close to condensing (low temperature, relatively high pressure), molecules move slowly and are relatively close together, making intermolecular attractive forces significant. These attractions pull molecules toward each other and away from the walls, reducing both the frequency of wall collisions and the momentum transferred per collision, resulting in lower measured pressure than ideal predictions. Choice C incorrectly claims the ideal gas law assumes particles have volume—it actually assumes negligible volume, and particle volume effects would increase (not decrease) pressure. The strategy is to recognize that conditions near condensation maximize attractive force effects, causing negative pressure deviations.
A gas sample is placed under conditions of very low pressure and high temperature. A student claims the gas will deviate strongly from $PV=nRT$ because the molecules are moving fast. Which statement best evaluates the claim?
Answer: The claim is incorrect because at low pressure and high temperature, intermolecular forces and particle volume are least significant, so behavior is closer to ideal. This question tests understanding of conditions that minimize deviations from ideal gas behavior. At low pressure and high temperature, gas molecules are far apart (large average separation) and moving rapidly (high kinetic energy). Under these conditions, intermolecular forces have minimal effect because molecules rarely come close enough to interact significantly, and particle volume is negligible compared to the large container volume. Therefore, the gas behaves nearly ideally, making the student's claim incorrect. Choice B incorrectly states that faster molecules experience stronger attractions - this represents a misconception conflating molecular speed with force strength, when actually higher speeds help molecules overcome weak attractive forces. To predict ideal behavior, remember that low pressure (molecules far apart) and high temperature (high kinetic energy) minimize both intermolecular force effects and particle volume effects.
A student is comparing the behavior of a real gas in a rigid container at (i) low pressure and high temperature versus (ii) high pressure and low temperature. The student finds that the gas behaves much more ideally in case (i) than in case (ii). Which statement best explains the difference in behavior?
Answer: Gases are more ideal at low pressure and high temperature because particles are far apart and move fast, minimizing attractions and the effect of particle volume. This question tests understanding of conditions that promote ideal gas behavior. Gases behave most ideally at low pressure and high temperature because these conditions maximize the average distance between particles and their kinetic energy. When particles are far apart (low pressure), intermolecular attractions become negligible, and particle volume is insignificant compared to container volume. High temperature gives particles high kinetic energy, allowing them to overcome weak attractions. Choice D incorrectly states that particle volume becomes a larger fraction at these conditions—actually, it becomes a smaller, negligible fraction. The strategy is to remember that ideal behavior requires minimizing both intermolecular forces and volume effects, achieved by keeping particles far apart and fast-moving.
A rigid container holds a sample of NH $_3$ (g) at very high pressure. Using $PV=nRT$ , a student calculates a pressure that is lower than what a pressure sensor actually reads. Which statement best explains why the real gas pressure is higher than the ideal prediction under these conditions?
Answer: The real pressure is higher because at high pressure the finite volume of gas particles reduces free space, increasing collision frequency with the walls. This question tests understanding of deviations from ideal gas behavior due to particle volume at high pressure. At very high pressure, gas molecules are compressed into a smaller space where the volume occupied by the particles themselves becomes significant compared to the container volume. Since the ideal gas law assumes point particles with zero volume, it uses the full container volume V in calculations, but real molecules can only move in the free space (V - volume of particles), leading to more frequent wall collisions and higher measured pressure than ideal predictions. Choice B incorrectly states that attractions would increase pressure, when attractions actually decrease pressure by reducing collision force. The strategy is to remember that high pressure makes particle volume effects dominant, causing positive deviations (real > ideal).
A sample of argon gas is placed in a container and cooled close to its condensation point while the pressure remains high. Relative to the pressure predicted by the ideal gas law for the same $n$ , $V$ , and $T$ , which deviation is most likely and what is the primary cause?
Answer: The real pressure is lower because intermolecular attractions reduce the force of collisions with the container walls compared with ideal behavior. This question tests the understanding of deviations from the ideal gas law due to intermolecular attractions becoming significant near the condensation point at low temperature. For argon cooled close to condensation with high pressure, the real pressure is lower than the ideal prediction because attractions pull molecules together, reducing the force and frequency of wall collisions compared to ideal behavior. The ideal gas law assumes no attractions, but at low temperature, these forces are pronounced, as captured by the attraction term in the van der Waals equation. High pressure is present, but the low temperature makes attractions the primary cause of deviation. A tempting distractor is choice C, which assumes noble gases always behave ideally due to being monatomic, ignoring that all real gases deviate under extreme conditions like low temperature. To solve these, recall that low temperature favors attraction deviations leading to lower real pressure, while checking for competing volume effects at high pressure.
A sealed syringe contains a sample of carbon dioxide gas. The gas is compressed to a very small volume at a moderately low temperature (still gaseous). Compared with the volume predicted by the ideal gas law at the same measured $P$ , $n$ , and $T$ , how will the real gas volume differ and why?
Answer: The real volume is larger because particle volume becomes significant at high pressure, so the gas occupies more space than the ideal model assumes. This question tests the understanding of deviations from the ideal gas law due to the finite volume of gas molecules affecting compressibility at high pressure. For carbon dioxide compressed to a small volume at moderately low temperature, the real volume is larger than the ideal prediction because the molecules occupy space, making the gas less compressible than the ideal model assumes. The ideal gas law calculates V = nRT/P assuming negligible molecular volume, but at high pressure, this leads to an underestimation of the actual volume needed to achieve the measured pressure. The van der Waals equation corrects for this by reducing the effective volume available for gas movement. A tempting distractor is choice A, which confuses the volume deviation with the attraction effect, mistakenly applying the attraction-dominant condition that makes volume smaller instead of the volume-dominant effect here. When predicting volume deviations, evaluate if high pressure conditions will make real volume larger due to molecular size excluding space.
A student cools a fixed amount of CH $_4$ (g) in a flexible container (like a balloon) to a very low temperature while the external pressure stays constant. The student uses ideal-gas reasoning to predict the volume but observes that the actual volume is smaller than predicted. Which statement best explains the deviation and its cause?
Answer: The actual volume is smaller because attractive intermolecular forces become more significant at low temperature, allowing the gas to occupy less volume at the same pressure. This question tests understanding of how intermolecular attractions affect gas volume at constant pressure and low temperature. At very low temperature, CH₄ molecules move slowly and attractive intermolecular forces (primarily London dispersion forces) become significant. These attractions pull molecules closer together, allowing the gas to occupy less volume than predicted by ideal gas law at the same external pressure—essentially, the attractions help the external pressure compress the gas more than expected for ideal particles. Choice D incorrectly states that gas particles have no volume, when the ideal gas law actually assumes particles have negligible (not zero) volume. The key insight is that at low temperature and constant pressure, attractive forces cause negative volume deviations (real < ideal).
Two gases, He(g) and SF $_6$ (g), are each placed in identical rigid containers at the same very low temperature and moderate-to-high pressure. A student uses $PV=nRT$ to predict the pressure for each gas but finds that SF $_6$ (g) shows a larger deviation from the ideal prediction. Which statement best explains why SF $_6$ (g) deviates more?
Answer: SF $_6$ (g) deviates more because its larger, more polarizable molecules experience stronger intermolecular attractions and have greater particle volume than He(g). This question tests understanding of why different gases show different magnitudes of deviation from ideal behavior. SF₆ is a much larger molecule than He, with more electrons making it more polarizable and capable of stronger London dispersion forces. Additionally, SF₆'s larger molecular volume becomes more significant at high pressure compared to tiny He atoms. These two factors—stronger intermolecular attractions and larger particle volume—cause SF₆ to deviate more from ideal behavior than He under the same conditions. Choice B incorrectly suggests the ideal gas law doesn't apply to high molar mass gases, when actually it applies to all gases but with varying accuracy. The key principle is that larger, more complex molecules with stronger intermolecular forces show greater deviations from ideality.
Two equal-mole samples, one of helium and one of chlorine gas, are placed in identical rigid containers at the same low temperature and relatively high pressure. A student uses $PV=nRT$ to predict the pressures and expects both to match. In practice, one sample shows a larger negative deviation (measured $P$ lower than ideal). Which statement best explains which sample deviates more and why?
Answer: Chlorine deviates more because its larger, more polarizable molecules have stronger attractions, lowering the measured pressure below ideal. This question tests understanding of how molecular properties affect deviations from ideal gas behavior. Chlorine molecules (Cl2) are much larger and more polarizable than helium atoms, resulting in stronger London dispersion forces between molecules. At low temperature and high pressure, these stronger intermolecular attractions in chlorine significantly reduce collision frequency and force with container walls, causing a larger negative deviation (lower measured pressure) compared to ideal predictions. Helium, being small and nonpolarizable, has very weak attractions and deviates less from ideal behavior under the same conditions. Choice B incorrectly claims smaller atoms have stronger attractions; polarizability and molecular size increase attraction strength. When comparing gas deviations, consider molecular properties: larger, more polarizable molecules always show greater deviations due to stronger intermolecular forces.
A student measures the compressibility factor $Z=\dfrac{PV}{nRT}$ for a real gas in a container at low temperature and moderately high pressure and finds $Z<1$ . Relative to ideal-gas behavior, what deviation and cause are most consistent with this result?
Answer: The gas has a lower effective pressure than ideal because intermolecular attractions dominate, making $PV$ smaller than $nRT$ . This question tests understanding of the compressibility factor and its relationship to deviations from ideal gas behavior. The compressibility factor Z = PV/nRT equals 1 for an ideal gas; when Z < 1, the product PV is less than nRT, indicating the gas is more compressible than ideal. At low temperature and moderately high pressure, intermolecular attractive forces dominate, pulling molecules together and reducing the effective pressure they exert on container walls, which makes PV < nRT and Z < 1. Choice C incorrectly attributes the deviation to particles having zero volume - this represents confusion about ideal gas assumptions, as having zero volume is actually an ideal gas assumption, not a cause of deviation. To interpret compressibility factors, remember that Z < 1 indicates attractive forces dominate (lower pressure than ideal), while Z > 1 indicates repulsive/volume effects dominate (higher pressure than ideal).
A sample of sulfur hexafluoride, $\mathrm{SF_6}$ , is held at high pressure in a container at room temperature. A student calculates the compressibility factor $Z=\dfrac{PV}{nRT}$ and finds $Z>1$ . Which interpretation best explains this result in terms of real-gas behavior?
Answer: $Z>1$ indicates repulsive effects and finite particle volume are significant, making the real gas less compressible than an ideal gas. This question tests understanding of the compressibility factor Z and its interpretation for real gases. When Z = PV/nRT > 1, the product PV is larger than predicted by ideal behavior, indicating the real gas is less compressible than an ideal gas. At high pressure, this occurs because gas particles have finite volume and experience short-range repulsions when forced close together. These repulsive effects and excluded volume make it harder to compress the gas further, resulting in higher pressure (or larger volume) than ideal predictions. SF6 is a large molecule, making particle volume effects particularly significant at high pressure. Choice B incorrectly claims Z>1 indicates attractive forces dominate; attractions would cause Z<1 by lowering pressure. To interpret compressibility factors, remember that Z>1 indicates repulsive/volume effects dominate (high P), while Z<1 indicates attractive forces dominate (low T, moderate P).
A rigid steel cylinder contains a sample of nitrogen gas that has been cooled to a very low temperature while also being compressed to a very high pressure. Compared with the pressure predicted by the ideal gas law for the same $n$ , $V$ , and $T$ , which statement best describes the real gas pressure and why?
Answer: The real pressure is higher because gas particles have finite volume that becomes significant at high pressure, increasing collision frequency with the container walls. This question tests the understanding of deviations from the ideal gas law due to the finite volume of gas molecules becoming significant under high pressure conditions. For nitrogen gas at very low temperature and very high pressure, the real pressure is higher than the ideal prediction because the molecules' own volume reduces the effective free space, leading to more frequent collisions with the container walls than assumed in the ideal model. The ideal gas law assumes point particles with no volume, but at high pressure, this assumption fails, and the correction in models like van der Waals accounts for this by subtracting a volume term. Although low temperature enhances attractions, the very high pressure makes the volume effect dominant in this scenario. A tempting distractor is choice D, which incorrectly states that attractive forces increase pressure by pulling molecules to the walls, misunderstanding that attractions actually decrease observed pressure by reducing collision force. To approach such problems, identify if conditions are high pressure (volume effect, higher real P) or low temperature/moderate pressure (attraction effect, lower real P).
A chemist compares measured and ideal-gas-law-predicted behavior for a sample of ammonia gas in a sealed container at low temperature and high pressure (still gaseous). Which statement best describes how the measured pressure compares with the ideal prediction and why?
Answer: The measured pressure is lower because intermolecular attractions (including hydrogen bonding) reduce the force of collisions with the walls compared with ideal behavior. This question tests the understanding of deviations from the ideal gas law due to strong intermolecular attractions, such as hydrogen bonding, at low temperature and high pressure. For ammonia at low temperature and high pressure, the measured pressure is lower than the ideal prediction because attractions, including hydrogen bonding, reduce collision force with the walls. The ideal gas law ignores these forces, but they are significant in polar molecules like ammonia under these conditions, leading to a lower observed pressure. Although high pressure is involved, the low temperature enhances attractions more than volume effects. A tempting distractor is choice A, which reverses the effect by claiming hydrogen bonding increases collision frequency and pressure, misunderstanding that attractions actually decrease pressure. When analyzing polar gases, consider how low temperature amplifies attraction deviations, resulting in lower real pressure.
A student compares O $_2$ (g) in a rigid container at room temperature and moderate pressure with O $_2$ (g) in the same container after it is compressed to a much higher pressure at the same temperature. The student notices that deviations from $PV=nRT$ become more noticeable after compression. Which statement best explains why?
Answer: Deviations increase because at higher pressure the finite volume of molecules and short-range repulsions become significant compared with the container volume. This question tests understanding of how compression increases deviations from ideal behavior. When O₂ is compressed to much higher pressure at constant temperature, molecules are forced closer together where two effects become significant: the finite volume of molecules reduces available free space, and short-range repulsive forces between electron clouds become important when molecules nearly touch. Both effects cause the measured pressure to exceed ideal predictions, with deviations increasing as compression increases. Choice B incorrectly states that attractions disappear at high pressure—actually, at very high pressure, repulsive forces dominate over attractions. The key principle is that increasing pressure magnifies non-ideal effects by reducing intermolecular distances.
Neon gas is compressed to extremely high pressure in a rigid container at room temperature. Compared with the volume predicted by the ideal gas law for the same $n$ , $T$ , and measured pressure, the real gas occupies a larger volume. What is the best reason for this behavior?
Answer: The real gas occupies a larger volume because the particles have finite volume that becomes significant when the gas is highly compressed. This question tests understanding of deviations from ideal gas behavior due to finite molecular volume. When neon is compressed to extremely high pressure, the volume occupied by the gas particles themselves becomes significant compared to the container volume. The ideal gas law assumes point particles with zero volume, but real gas particles have finite volume that cannot be compressed away. At extreme compression, this particle volume means the actual space available for molecular motion is less than the container volume, causing the real gas to occupy more volume than ideal predictions at the same pressure. Choice B incorrectly suggests attractions would decrease volume, but attractions actually lower pressure, not increase volume at constant pressure. When analyzing volume deviations at high pressure, remember that particle volume effects dominate over intermolecular attractions, making real gases less compressible than ideal gases.
A sample of methane gas is cooled and compressed until it is near conditions where liquefaction could occur. If a student uses the ideal gas law to predict the volume at the measured pressure and temperature, how will the real volume most likely compare and why?
Answer: The real volume is smaller because attractive intermolecular forces make the gas more compressible than the ideal model predicts under these conditions. This question tests the understanding of deviations from the ideal gas law due to intermolecular attractions making gases more compressible near liquefaction conditions. For methane cooled and compressed near liquefaction, the real volume is smaller than the ideal prediction because attractions allow tighter packing under pressure than the ideal model assumes. The ideal gas law V = nRT/P overestimates volume since real pressure is lower due to attractions, so the actual volume for the measured pressure is smaller. This is prominent near liquefaction where attractions dominate. A tempting distractor is choice C, which assumes nonpolar gases like methane behave ideally, ignoring that all gases deviate under low-temperature, high-pressure conditions. To predict volume deviations, assess if attractions (smaller real V) or volume effects (larger real V) prevail based on temperature and pressure.
A fixed amount of a real gas is placed in a rigid container. The gas is then cooled significantly while the volume remains constant. The student observes that the measured pressure drops more than predicted by $PV=nRT$ . Which explanation best accounts for this behavior?
Answer: The pressure drops more because attractive intermolecular forces become more important at lower temperature, reducing wall-collision force beyond ideal predictions. This question tests understanding of temperature effects on deviations from ideal gas behavior. When a real gas is cooled significantly at constant volume, the ideal gas law predicts pressure drops proportionally to temperature (P ∝ T). However, at lower temperature, molecules move more slowly and spend more time near each other, allowing attractive intermolecular forces to become more significant. These attractions reduce the force of molecular collisions with walls beyond what slower motion alone would cause, making the actual pressure drop more than the ideal prediction. Choice E incorrectly suggests particle volume increases at low temperature, when molecular size remains constant regardless of temperature. The strategy is to remember that cooling enhances attractive force effects, causing extra pressure reduction beyond ideal predictions.
A student compares equal amounts of helium gas and xenon gas in identical rigid containers at the same low temperature and moderately high pressure. The student uses the ideal gas law to predict the pressure for each gas. Which statement best describes which gas deviates more from ideal behavior and why?
Answer: Xenon deviates more because it has stronger intermolecular attractions and larger particle size. This question tests understanding of how molecular properties affect deviations from ideal gas behavior. Xenon, being much larger and more polarizable than helium, has stronger London dispersion forces and occupies more volume per atom. At low temperature and moderately high pressure, both intermolecular attractions and particle volume contribute to deviations from ideal behavior. Xenon's stronger attractions reduce pressure below ideal predictions, while its larger size reduces available free volume, increasing pressure above ideal predictions. The net deviation for xenon is greater than for helium, which has minimal attractions and negligible volume. Choice A incorrectly invokes gravitational attraction, which is insignificant for gas molecules. When comparing gases, consider both molecular size and polarizability - larger, more polarizable atoms like xenon deviate more from ideal behavior under conditions that enhance these effects.
A container holds a real gas at very low temperature and moderate pressure, and the gas particles are moving relatively slowly. Compared with the ideal-gas-law prediction for pressure at the same $n$ , $V$ , and $T$ , which deviation is most likely and what causes it?
Answer: The real pressure is lower because attractive intermolecular forces become more significant at low temperature and reduce the force of wall collisions. This question tests the understanding of deviations from the ideal gas law due to intermolecular attractions at very low temperature and moderate pressure. For a real gas at very low temperature and moderate pressure with slow-moving particles, the real pressure is lower than the ideal prediction because attractions reduce collision force with the walls. The ideal gas law assumes no forces, but low kinetic energy at low temperature allows attractions to dominate, as in van der Waals corrections. Moderate pressure minimizes volume effects. A tempting distractor is choice A, which claims slower particles increase pressure via more collisions, misunderstanding that slower speed actually decreases pressure impact while attractions further reduce it. Always evaluate temperature first: low T often means attraction deviations and lower real pressure.

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