Deviation from Ideal Gas Law
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AP Chemistry › Deviation from Ideal Gas Law
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?
The real pressure is higher because at high pressure the finite volume of gas particles reduces free space, increasing collision frequency with the walls.
The real pressure is higher because $PV=nRT$ only applies when temperature is changing, not when pressure is high.
The real pressure is higher because NH$_3$ decomposes into N$_2$ and H$_2$ at high pressure, increasing $n$ and raising pressure.
The real pressure is higher because strong attractions at high pressure pull molecules away from the walls, decreasing collisions and increasing pressure.
The real pressure is higher because the ideal gas law assumes particles have volume, so it underestimates pressure at high pressure.
Explanation
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 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?
The pressure drops more because particle volume increases at low temperature, leaving more free space and lowering pressure.
The pressure drops more because the ideal gas law assumes molecules attract, so it overestimates pressure when attractions increase.
The pressure drops more because attractive intermolecular forces become more important at lower temperature, reducing wall-collision force beyond ideal predictions.
The pressure drops more because lower temperature increases molecular speed, which reduces the pressure compared with ideal predictions.
The pressure drops more because the gas chemically decomposes upon cooling, decreasing $n$ and causing extra pressure loss.
Explanation
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 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?
The actual volume is smaller because gas particles have no volume, so at low temperature the container must shrink to keep $PV$ constant.
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.
The actual volume is smaller because repulsive forces increase at low temperature, pushing molecules apart and decreasing volume.
The actual volume is smaller because CH$_4$ reacts with air in the balloon, decreasing $n$ and forcing the volume to shrink below ideal.
The actual volume is smaller because the ideal gas law assumes strong attractions, so it overestimates volume at low temperature.
Explanation
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).
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?
The real volume is smaller because attractive forces pull molecules closer together, making the gas more compressible than predicted by the ideal model.
The real volume is smaller because the pressure gauge reads too high at low temperature, which makes the ideal calculation overestimate volume.
The real volume is larger because particle volume becomes significant at high pressure, so the gas occupies more space than the ideal model assumes.
The real volume is larger because compression causes CO$_2$ to decompose into CO and O$_2$, increasing the number of moles of gas.
The real volume equals the ideal prediction because deviations occur only for gases with polar molecules, and CO$_2$ is nonpolar.
Explanation
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 real gas is compressed to very high pressure in a piston-cylinder apparatus while kept at a temperature high enough that condensation is not likely. Compared with the volume predicted by the ideal gas law at the same $P$, $n$, and $T$, how will the real gas volume most likely differ and why?
The real volume is larger because finite particle volume becomes important at high pressure, so the gas cannot be compressed as much as the ideal model predicts.
The real volume equals the ideal prediction because high temperature eliminates all deviations from ideal behavior at any pressure.
The real volume is smaller because compression increases the number of moles of gas, so less volume is needed at fixed pressure.
The real volume is larger because the ideal gas law assumes particles attract each other strongly, which makes the ideal prediction too small.
The real volume is smaller because at high pressure attractive forces dominate, pulling particles closer and decreasing volume below ideal.
Explanation
This question tests the understanding of deviations from the ideal gas law due to finite molecular volume at very high pressure and high temperature. For a real gas compressed to very high pressure at high temperature avoiding condensation, the real volume is larger than the ideal prediction because particle volume limits compression beyond ideal assumptions. The ideal V = nRT/P underestimates volume since real gases resist compression due to occupied space, especially at high pressure. High temperature reduces attractions, letting volume effects dominate. A tempting distractor is choice A, which misapplies attraction effects to high pressure, confusing it with low-temperature scenarios where volume is smaller. To differentiate, note high temperature and pressure favor volume deviations, leading to larger real volumes.
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?
The gas has a higher effective pressure than ideal because intermolecular attractions dominate, making $PV$ larger than $nRT$.
The gas has a higher effective pressure than ideal because the gas particles have zero volume, making $PV$ larger than $nRT$.
The gas has a lower effective pressure than ideal because intermolecular attractions dominate, making $PV$ smaller than $nRT$.
The gas matches ideal behavior because $Z<1$ indicates the ideal gas law is exact under all conditions.
The gas has a lower effective pressure than ideal because the gas particles have zero volume, making $PV$ smaller than $nRT$.
Explanation
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).
Argon gas is placed in a container and compressed to a very small volume while the temperature is kept constant. A student applies the ideal gas law to predict the pressure. Compared with the ideal prediction, which outcome is most consistent with real-gas behavior under these conditions, and why?
The real pressure is the same because noble gases never deviate from ideal behavior at any pressure.
The real pressure is higher because the gas reacts with the container, producing additional gas molecules.
The real pressure is lower because compressing the gas increases attractions enough to eliminate pressure entirely.
The real pressure is higher because particle volume becomes significant compared with the container volume.
The real pressure is lower because argon forms temporary covalent bonds that reduce collisions with the walls.
Explanation
This question tests understanding of deviations from ideal gas behavior due to particle volume under extreme compression. When argon is compressed to a very small volume at constant temperature, the volume occupied by the argon atoms themselves becomes a significant fraction of the total container volume. The ideal gas law assumes particles have zero volume, but real particles exclude other particles from the space they occupy. This excluded volume effect means the actual free space for particle movement is less than the container volume V, causing more frequent wall collisions and higher pressure than predicted. Choice A incorrectly suggests argon forms covalent bonds, which noble gases do not do under normal conditions. To predict volume-related deviations, consider the ratio of particle volume to container volume - extreme compression makes this ratio significant, increasing pressure above 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?
Xenon deviates less because heavier gases have fewer collisions and therefore behave more ideally.
Both deviate equally because the ideal gas law includes a universal correction for all gases.
Helium deviates more because noble gases are always non-ideal at any temperature.
Xenon deviates more because it has stronger intermolecular attractions and larger particle size.
Helium deviates more because its smaller molar mass increases gravitational attraction between particles.
Explanation
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.
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?
The real gas occupies a larger volume because the particles have finite volume that becomes significant when the gas is highly compressed.
The real gas occupies a larger volume because the molar mass of neon increases at high pressure, requiring more space per mole.
The real gas occupies a larger volume because stronger attractions at high pressure pull particles closer, decreasing the volume below ideal.
The real gas occupies a larger volume because some neon liquefies, increasing the measured gas volume above ideal.
The real gas occupies a larger volume because ideal gas theory already includes particle volume, so deviations must be chemical in origin.
Explanation
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 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?
Gases are more ideal at low pressure and high temperature because particle volume becomes a larger fraction of the container volume.
Gases are more ideal at low pressure and high temperature because stronger attractions form, making collisions more elastic and more ideal.
Gases are more ideal at low pressure and high temperature because the ideal gas law only applies when pressure is low, regardless of temperature.
Gases are more ideal at low pressure and high temperature because chemical reactions stop, and ideal behavior requires no reactions.
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.
Explanation
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.