Deviation from Ideal Gas Law
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AP Chemistry › Deviation from Ideal Gas Law
A sample of N$_2$(g) is compressed into a small rigid container at very high pressure while the temperature is held constant. Compared with the pressure predicted by $PV=nRT$, the measured pressure is higher. Which reasoning best accounts for this observation?
At high pressure, the gas becomes ideal because the molecules are closer together and behave more like point particles.
At high pressure, particle volume becomes significant so the available volume for motion is smaller than $V$, leading to more frequent wall collisions and higher pressure.
At high pressure, N$_2$ undergoes an endothermic reaction that increases temperature, which increases pressure beyond the ideal prediction.
At high pressure, attractive forces dominate and pull molecules toward the center, increasing the measured pressure above ideal.
At high pressure, $n$ decreases because molecules merge, so the ideal gas law overpredicts pressure and the measured value is higher.
Explanation
This question tests understanding of positive deviations from ideal gas behavior at high pressure. When N₂ is compressed to very high pressure, the molecules are forced close together where their finite volume becomes significant. The ideal gas law assumes point particles can access the full container volume V, but real molecules exclude some volume, leaving less free space for movement (V_free = V - V_particles). This reduced free space causes molecules to collide with walls more frequently, resulting in higher measured pressure than ideal predictions. Choice B incorrectly suggests attractions would increase pressure, when attractions actually decrease it by reducing collision momentum. The strategy is to recognize that at very high pressure, volume exclusion dominates over attractive forces, causing measured pressure to exceed ideal predictions.
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 particles are far apart and move fast, minimizing attractions and the effect of particle volume.
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.
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.
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?
The measured pressure is lower because the ideal gas law assumes particles have volume, which makes it overpredict pressure at low temperature.
The measured pressure is lower because at high pressure gases always behave more ideally, so the sensor must be miscalibrated.
The measured pressure is lower because intermolecular attractions reduce the momentum transferred to the container walls, lowering pressure relative to ideal.
The measured pressure is lower because the gas particles become massless at low temperature, decreasing pressure relative to ideal.
The measured pressure is lower because the gas undergoes a chemical reaction that consumes heat, and lower heat content always lowers pressure.
Explanation
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 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?
Deviations increase because at higher pressure the finite volume of molecules and short-range repulsions become significant compared with the container volume.
Deviations increase because higher pressure lowers the temperature, and the ideal gas law assumes temperature is constant.
Deviations increase because compression causes O$_2$ to chemically react to form O$_3$, increasing $n$ and invalidating the ideal gas law.
Deviations increase because the ideal gas law only applies to diatomic gases at low pressure, and compression changes O$_2$ into a different type of gas.
Deviations increase because at higher pressure intermolecular attractions disappear, causing the gas to become non-ideal.
Explanation
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.
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 NH$_3$ decomposes into N$_2$ and H$_2$ at high pressure, increasing $n$ and raising pressure.
The real pressure is higher because the ideal gas law assumes particles have volume, so it underestimates pressure at high pressure.
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 strong attractions at high pressure pull molecules away from the walls, decreasing collisions and increasing pressure.
The real pressure is higher because $PV=nRT$ only applies when temperature is changing, not when pressure is high.
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 lower temperature increases molecular speed, which reduces the pressure compared with ideal predictions.
The pressure drops more because the ideal gas law assumes molecules attract, so it overestimates pressure when attractions increase.
The pressure drops more because the gas chemically decomposes upon cooling, decreasing $n$ and causing extra pressure loss.
The pressure drops more because attractive intermolecular forces become more important at lower temperature, reducing wall-collision force beyond ideal predictions.
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 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 the ideal gas law assumes strong attractions, so it overestimates volume at low temperature.
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 CH$_4$ reacts with air in the balloon, decreasing $n$ and forcing the volume to shrink below ideal.
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 larger because particle volume becomes significant at high pressure, so the gas occupies more space than the ideal model assumes.
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 smaller because attractive forces pull molecules closer together, making the gas more compressible than predicted by the ideal model.
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 student collects sulfur dioxide gas in a container under conditions of high pressure and low temperature (still gaseous). When comparing the measured pressure to the pressure predicted by the ideal gas law for the same $n$, $V$, and $T$, which statement best accounts for any difference?
The measured pressure is higher because attractive forces dominate at low temperature and push molecules into the walls more strongly than ideal behavior.
The measured pressure is lower because SO$_2$ disproportionates into sulfur and oxygen, lowering the number of gas molecules.
The measured pressure equals the ideal prediction because SO$_2$ is a molecular compound and molecular gases are ideal.
The measured pressure is higher because SO$_2$ molecules occupy no volume, so the ideal gas law underestimates pressure at high pressure.
The measured pressure is lower because intermolecular attractions reduce the effective pressure compared with the ideal gas law prediction.
Explanation
This question tests the understanding of deviations from the ideal gas law due to intermolecular attractions in polar gases like SO2 at high pressure and low temperature. For sulfur dioxide at high pressure and low temperature, the measured pressure is lower than the ideal prediction because attractions reduce effective pressure by weakening wall collisions. The ideal gas law overlooks these forces, which are strong in SO2 due to polarity, and low temperature enhances this effect despite high pressure. Van der Waals accounts for this with an attraction term. A tempting distractor is choice A, which incorrectly states attractions increase pressure by pushing to walls, reversing the actual effect of attractions lowering pressure. For polar gases, prioritize attraction effects at low temperature, even with high pressure, to predict lower real pressure.
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?
The measured pressure is lower because intermolecular attractions (including hydrogen bonding) reduce the force of collisions with the walls compared with ideal behavior.
The measured pressure equals the ideal prediction because ammonia is a gas and all gases obey $PV=nRT$ exactly.
The measured pressure is lower because high pressure reduces the temperature of the gas, making the ideal calculation too large.
The measured pressure is higher because ammonia decomposes at low temperature to form more moles of gas, increasing pressure.
The measured pressure is higher because hydrogen bonding increases the frequency of collisions with the walls beyond ideal predictions.
Explanation
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.